Dissertations / Theses on the topic 'Stochastic orders'
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Dong, Jing, and 董靜. "On upper comonotonicity and stochastic orders." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B43085453.
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Dong, Jing. "On upper comonotonicity and stochastic orders." Click to view the E-thesis via HKUTO, 2009. http://sunzi.lib.hku.hk/hkuto/record/B43085453.
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Wong, Tityik 1962. "Contributions to the theory of stochastic orders." Diss., The University of Arizona, 1996. http://hdl.handle.net/10150/290627.
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This dissertation adds some new results to the theory of stochastic orders. Chapter 1 contains definitions and known results that are related to our study. In Chapter 2, we introduce two new stochastic orders based on ratios of Laplace transforms, and study various properties of the new orders. Among the many properties we discover, the most interesting ones are the relations between the new orders and some existing stochastic orders. In Chapter 3, we obtain various stochastic comparison results of random extrema, that is, the maxima and minima of samples with random sizes. Some results in Chapter 2 find their applications here. In Chapter 4, we study the preservation of various stochastic orders (including the new orders introduced in Chapter 2) under random mapping by point processes. Chapter 5 contains results concerning the preservation of multivariate stochastic orders under shock models. In Chapter 6 we study the preservation of multivariate stochastic orders under random mapping by point processes. Examples and applications of main theorems are presented throughout the dissertation.
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Xu, Maochao. "Stochastic Orders in Heterogeneous Samples with Applications." PDXScholar, 2010. https://pdxscholar.library.pdx.edu/open_access_etds/391.
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The statistics literature has mostly focused on the case when the data available is in the form of a random sample. In many cases, the observations are not identically distributed. Such samples are called heterogeneous samples. The study of heterogeneous samples is of great interest in many areas, such as statistics, econometrics, reliability engineering, operation research and risk analysis. Stochastic orders between probability distributions is a widely studied concept. There are several kinds of stochastic orders that are used to compare different aspects of probability distributions like location, variability, skewness, dependence, etc. In this dissertation, most of the work is devoted to investigating the properties of statistics based on heterogeneous samples with the aid of stochastic orders. We will see the effect of the change in the stochastic properties of various functions of observations as their parameters change. The theory of majorization will be used for this purpose. First, order statistics from heterogeneous samples will be investigated. Order statistics appear everywhere in statistics and related areas. The k-out-of-n systems are building blocks of a coherent system. The lifetime of such a system is the same as that of the (n-k+1)th order statistic in a sample size of n. Stochastic comparisons between order statistics have been studied extensively in the literature in case the parent observations are independent and identically distributed. However, in practice this assumption is often violated as different components in a system may not have the same distribution. Comparatively less work has been done in the case of heterogeneous random variables, mainly because of the reason that their distribution theory is very complicated. Some open problems in the literature have been solved in the dissertation. Some new problems associated with order statistics have been investigated in the thesis. Next, stochastic properties of spacings based on heterogeneous observations are studied. Spacings are of great interest in many areas of statistics, in particular, in the characterizations of distributions, goodness-of-fit tests, life testing and reliability models. In particular, the stochastic properties of the sample range are investigated in detail. Applications in reliability theory are highlighted. The relative dependence between extreme order statistics will be investigated in Chapter 4. In particular, the open problem discussed in Dolati, et al. (2008) is solved in this Chapter. In the last Chapter, convolutions of random variables from heterogeneous samples will be investigated. Convolutions have been widely used in many areas to model many practical situations. For example, in reliability theory, it arises as the lifetime of a redundant standby system; in queuing theory, it is used to model the total service time by an agent in a system; in insurance, it is used to model total claims on a number of policies in the individual risk model. I will compare the dispersion and skewness properties of convolutions of different heterogeneous samples. The tail behavior of convolutions are investigated as well. The work in this dissertation has significant applications in many diverse areas of applied probability and statistics. For example, statistics based on order statistics and spacings from heterogeneous samples arise in studying the robust properties of statistical procedures; the work on order statistics will also provide a better estimation of lifetime of a coherent system in reliability engineering; convolution results will be of great interest in insurance and actuarial science for evaluating risks.
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Zeng, Xin. "Comparative Statics Analysis of Some Operations Management Problems." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/39178.
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We propose a novel analytic approach for the comparative statics analysis of
operations management problems on the capacity investment decision and the
influenza (flu) vaccine composition decision. Our approach involves exploiting
the properties of the underlying mathematical models, and linking those
properties to the concept of stochastic orders relationship. The use of
stochastic orders allows us to establish our main results without restriction
to a specific distribution. A major strength of our approach is that it is
"scalable," i.e., it applies to capacity investment decision problem with any
number of â non-independentâ (i.e., demand or resource sharing) products and
resources, and to the influenza vaccine composition problem with any number of
candidate strains, without a corresponding increase in computational effort.
This is unlike the current approaches commonly used in the operations
management literature, which typically involve a parametric analysis followed
by the use of the implicit function theorem. Providing a rigorous framework
for comparative statics analysis, which can be applied to other problems that
are not amenable to traditional parametric analysis, is our main contribution.
We demonstrate this approach on two problems: (1) Capacity investment
decision, and (2) influenza vaccine composition decision. A comparative
statics analysis is integral to the study of these problems, as it allows
answers to important questions such as, "does the firm acquire more or less
of the different resources available as demand uncertainty increases? does the
firm benefit from an increase in demand uncertainty? how does the vaccine
composition change as the yield uncertainty increases?" Using our proposed
approach, we establish comparative statics results on how the newsvendor's
expected profit and optimal capacity decision change with demand risk and
demand dependence in multi-product multi-resource newsvendor networks; and how
the societal vaccination benefit, the manufacturer's profit, and the vaccine
output change with the risk of random yield of strains.Ph. D.
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Liu, Yunfeng. "Tests of Bivariate Stochastic Order." Thèse, Université d'Ottawa / University of Ottawa, 2011. http://hdl.handle.net/10393/20257.
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The purpose of this thesis is to compare rank-based tests of bivariate stochastic order. Given two bivariate distributions $F$ and $G$, the general problem we are dealing with is to test $H_0: F=G$ against $H_1:F
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Naujokat, Felix. "Stochastic control in limit order markets." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2011. http://dx.doi.org/10.18452/16387.
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In dieser Dissertation lösen wir eine Klasse stochastischer Kontrollprobleme und konstruieren optimale Handelsstrategien in illiquiden Märkten. In Kapitel 1 betrachten wir einen Investor, der sein Portfolio nahe an einer stochastischen Zielfunktion halten möchte. Gesucht ist eine Strategie (aus aktiven und passiven Orders), die die Abweichung vom Zielportfolio und die Handelskosten minimiert. Wir zeigen Existenz und Eindeutigkeit einer optimalen Strategie. Wir beweisen eine Version des stochastischen Maximumprinzips und leiten damit ein Kriterium für Optimalität mittels einer gekoppelten FBSDE her. Wir beweisen eine zweite Charakterisierung mittels Kauf- und Verkaufregionen. Das Portfolioliquidierungsproblem wird explizit gelöst. In Kapitel 2 verallgemeinern wir die Klasse der zulässigen Strategien auf singuläre Marktorders. Wie zuvor zeigen wir Existenz und Eindeutigkeit einer optimalen Strategie. Im zweiten Schritt beweisen wir eine Version des Maximumprinzips im singulären Fall, die eine notwendige und hinreichende Optimalitätsbedingung liefert. Daraus leiten wir eine weitere Charakterisierung mittels Kauf-, Verkaufs- und Nichthandelsregionen ab. Wir zeigen, dass Marktorders nur benutzt werden, wenn der Spread klein genug ist. Wir schließen dieses Kapitel mit einer Fallstudie über Portfolioliquidierung ab. Das dritte Kapitel thematisiert Marktmanipulation in illiquiden Märkten. Wenn Transaktionen einen Einfluß auf den Aktienpreis haben, dann können Optionsbesitzer damit den Wert ihres Portfolios beeinflussen. Wir betrachten mehrere Agenten, die europäische Derivate halten und den Preis des zugrundeliegenden Wertpapiers beeinflussen. Wir beschränken uns auf risikoneutrale und CARA-Investoren und zeigen die Existenz eines eindeutigen Gleichgewichts, das wir mittels eines gekoppelten Systems nichtlinearer PDEs charakterisieren. Abschließend geben wir Bedingungen an, wie diese Art von Marktmanipulation verhindert werden kann.In this thesis we study a class of stochastic control problems and analyse optimal trading strategies in limit order markets. The first chapter addresses the problem of curve following. We consider an investor who wants to keep his stock holdings close to a stochastic target function. We construct the optimal strategy (comprising market and passive orders) which balances the penalty for deviating and the cost of trading. We first prove existence and uniqueness of an optimal control. The optimal trading strategy is then characterised in terms of the solution to a coupled FBSDE involving jumps via a stochastic maximum principle. We give a second characterisation in terms of buy and sell regions. The application of portfolio liquidation is studied in detail. In the second chapter, we extend our results to singular market orders using techniques of singular stochastic control. We first show existence and uniqueness of an optimal control. We then derive a version of the stochastic maximum principle which yields a characterisation of the optimal trading strategy in terms of a nonstandard coupled FBSDE. We show that the optimal control can be characterised via buy, sell and no-trade regions. We describe precisely when it is optimal to cross the bid ask spread. We also show that the controlled system can be described in terms of a reflected BSDE. As an application, we solve the portfolio liquidation problem with passive orders. When markets are illiquid, option holders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. In Chapter 3, we consider a model with competing players that hold European options and whose trading has an impact on the price of the underlying. We establish existence and uniqueness of equilibrium results and show that the equilibrium dynamics can be characterised in terms of a coupled system of non-linear PDEs. Finally, we show how market manipulation can be reduced.
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Locatelli, Marco. "Order reduction strategies for stochastic Galerkin matrix equations." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/15881/.
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Lo scopo di questa tesi è l'implementazione di un algoritmo in grado di risolvere in maniera efficiente sistemi lineari provenienti da un'approssimazione agli elementi finiti di Galerkin stocastica di equazioni alle derivate parziali con dati aleatori.
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Dutt, Arkopal. "High order stochastic transport and Lagrangian data assimilation." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/115663.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 103-113).
Ocean currents transport a variety of natural (e.g. water masses, phytoplankton, zooplankton, sediments, etc.) and man-made materials (e.g. pollutants, floating debris, particulate matter, etc.). Understanding such uncertain Lagrangian transport is imperative for reducing environmental damage due to natural hazards and for allowing rigorous risk analysis and effective search and rescue. While secondary variables and trajectories have classically been used for the analyses of such transports, Lagrangian Coherent Structures (LCSs) provide a robust and objective description of the important material lines. To ensure accurate and useful Lagrangian hazard scenario predictions and prevention, the first goal of this thesis is to obtain accurate probabilistic prediction of the underlying stochastic velocity fields using the Dynamically Orthogonal (DO) approach. The second goal is to merge data from both Eulerian and Lagrangian observations with predictions such that the whole information content of observations is utilized. In the first part of this thesis, we develop high-order numerical schemes for the DO equations that ensure efficiency, accuracy, stability, and consistency between the Monte Carlo (MC) and DO solutions. We discuss the numerical challenges in applying the DO equations to the unsteady stochastic Navier-Stokes equations. In order to maintain consistent evaluation of advection terms, we utilize linear centered advection schemes with fully explicit and linear Shapiro filters. We then discuss how to combine the semi-implicit projection method with new high order implicitexplicit (IMEX) linear multi-step and multistage IMEX-RK time marching schemes for the coupled DO equations to ensure further stability and accuracy. We also review efficient numerical re-orthonormalization strategies during time marching. We showcase our results with stochastic test cases of stochastic passive tracer advection in a deterministic swirl flow, stochastic flow past a cylinder, and stochastic lid-driven cavity flow. We show that our schemes improve the consistency between reconstructed DO realizations and the corresponding MC realizations, and that we achieve the expected order of accuracy. In the second part of the work, we first undertake a study of different Lagrangian instruments and outline how the DO methodology can be applied to obtain Lagrangian variables of stochastic flow maps and LCS in uncertain flows. We then review existing methods for Bayesian Lagrangian data assimilation (DA). Disadvantages of earlier methods include the use of approximate measurement models to directly link Lagrangian variables with Eulerian variables, the challenges in respecting the Lagrangian nature of variables, and the assumptions of linearity or of Gaussian statistics during prediction or assimilation. To overcome these, we discuss how the Gaussian Mixture Model (GMM) DO Filter can be extended to fully coupled Eulerian-Lagrangian data assimilation. We define an augmented state vector of the Eulerian and Lagrangian state variables that directly exploits the full mutual information and complete the Bayesian DA in the joint Eulerian-Lagrangian stochastic subspace. Results of such coupled Eulerian-Lagrangian DA are discussed using test cases based on a double gyre flow with random frequency.
by Arkopal Dutt.
S.M.
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Kosuch, Stefanie. "Stochastic Optimization Problems with Knapsack Constraint." Paris 11, 2010. http://www.theses.fr/2010PA112154.
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Etant donné un ensemble d'objets, chacun ayant un poids et une valeur. Le problème de sac-à-dos consiste à choisir un sous-ensemble d'objets qui (i) respecte une certaine restriction du poids (la capacité du sac-à-dos) et (ii) dont la valeur totale est maximisée. Dans cette thèse nous étudions quatre problèmes d'optimisation stochastique avec contrainte de sac-à-dos: le problème de sac-à-dos avec recours simple, le problème de sac-à-dos avec contrainte probabiliste, le problème de sac-à-dos avec recours et un problème bi-niveau stochastique avec contrainte de sac-à-dos probabiliste. Les problèmes ont en commun que les poids dans la contrainte de sac-à-dos sont supposés être aléatoires. Nous proposons de résoudre les problèmes du sac-à-dos avec recours simple ou avec contrainte probabiliste en appliquant un algorithme « branch-and-bound ». Des bornes supérieures sont obtenues en résolvant des relaxations continues. Pour ceci, nous appliquons un algorithme de gradient stochastique. Concernant le cas du sac-à-dos avec recours, nous traitons dans un premier temps le problème avec des poids gaussiens et nous proposons des bornes inférieures et supérieures sur sa valeur optimale. Dans un deuxième temps, nous étudions le cas d’une distribution discrète des poids. Nous montrons que (si P n'est pas égal à NP) le problème déterministe équivalent n’admet pas d’algorithme d’approximation avec une garantie de performance égale à une valeur constante. Le problème bi-niveau stochastique avec contrainte de sac-à-dos probabiliste est d’abord reformulé comme un problème bilinéaire. Ce dernier étant difficile à résoudre à l’optimum, nous proposons de résoudre une relaxation avec un nouvel algorithme itératifGiven a set of objects each having a particular weight and value. The knapsack problem consists of choosing among these items a subset such that (i) the total weight of the chosen items does respect a given weight constraint (the capacity of the knapsack) and (ii) the total value of the chosen items is maximized. In this thesis, we study four stochastic optimization problems with knapsack constraint: the simple recourse knapsack problem, the chance-constrained knapsack problem, the two-stage knapsack problem and a bilievel problem with knapsack chance-constraint. All problems have in common that the item weights in the knapsack constraints are assumed to be random. We propose to solve the simple recourse and the chance-constrained knapsack problems using a branch-&-bound algorithm as framework. Upper bounds are obtained by solving relaxed, i. E. Continuous sub-problems. The latter is done by applying a stochastic gradient algorithm. Concerning the two-stage knapsack problem, we treat, in the first instance, the model where the item weights are assumed to be normally distributed and propose upper and lower bounds on the optimal solution value. Then, we study the problem with discretely distributed weights and show that its deterministic equivalent reformulation does not admit a constant factor approximation algorithm unless P=NP. The studied bilevel problem with knapsack chance-constraint is first of all reformulated as a deterministic equivalent bilinear problem. As the latter is generally hard to solve exactly, we propose to solve a relaxation using a novel iterative algorithm
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Hagerlind, Simon. "Empirical evaluation of a stochastic model for order book dynamics." Thesis, Uppsala universitet, Matematiska institutionen, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-181603.
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Abstract A stochastic model for orderbook dynamics is proposed in Cont et al.(2010) and empirically evaluated in thisthesis. Arrival rates of limit, marketand cancellation orders are described interms of a Markov chain where thearrival rates are exponentiallydistributed. The model not onlyconsiders the best bid and ask queuesbut also additional price levels of theorder book. Methods for computingseveral quantities important to highfrequency trading are proposed usingLaplace transforms and continuedfractions. These quantities includeconditional probabilities such as theprobability of a price increasedepending on the profile of the orderbook. Computing these probabilities aresupposed to be easy enough to computeanalytically. However this was not thecase. We failed in the inversion of theLaplace transform methods and the mainreason is that the instructions in Contet al. (2010) are not adequate when itcomes to perform the inversion. Hence wedraw the conclusion that the method isno good for predicting short termbehavior of limit order books. For longterm applications the model can be usedto simulate the order book with goodresults.
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Noubiagain, Chomchie Fanny Larissa. "Contributions to second order reflected backward stochastic differentials equations." Thesis, Le Mans, 2017. http://www.theses.fr/2017LEMA1016/document.
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Cette thèse traite des équations différentielles stochastiques rétrogrades réfléchies du second ordre dans une filtration générale . Nous avons traité tout d'abord la réflexion à une barrière inférieure puis nous avons étendu le résultat dans le cas d'une barrière supérieure. Notre contribution consiste à démontrer l'existence et l'unicité de la solution de ces équations dans le cadre d'une filtration générale sous des hypothèses faibles. Nous remplaçons la régularité uniforme par la régularité de type Borel. Le principe de programmation dynamique pour le problème de contrôle stochastique robuste est donc démontré sous les hypothèses faibles c'est à dire sans régularité sur le générateur, la condition terminal et la barrière. Dans le cadre des Équations Différentielles Stochastiques Rétrogrades (EDSRs ) standard, les problèmes de réflexions à barrières inférieures et supérieures sont symétriques. Par contre dans le cadre des EDSRs de second ordre, cette symétrie n'est plus valable à cause des la non linéarité de l'espérance sous laquelle est définie notre problème de contrôle stochastique robuste non dominé. Ensuite nous un schéma d'approximation numérique d'une classe d'EDSR de second ordre réfléchies. En particulier nous montrons la convergence de schéma et nous testons numériquement les résultats obtenusThis thesis deals with the second-order reflected backward stochastic differential equations (2RBSDEs) in general filtration. In the first part , we consider the reflection with a lower obstacle and then extended the result in the case of an upper obstacle . Our main contribution consists in demonstrating the existence and the uniqueness of the solution of these equations defined in the general filtration under weak assumptions. We replace the uniform regularity by the Borel regularity(through analytic measurability). The dynamic programming principle for the robust stochastic control problem is thus demonstrated under weak assumptions, that is to say without regularity on the generator, the terminal condition and the obstacle. In the standard Backward Stochastic Differential Equations (BSDEs) framework, there is a symmetry between lower and upper obstacles reflection problem. On the contrary, in the context of second order BSDEs, this symmetry is no longer satisfy because of the nonlinearity of the expectation under which our robust stochastic non-dominated stochastic control problem is defined. In the second part , we get a numerical approximation scheme of a class of second-order reflected BSDEs. In particular we show the convergence of our scheme and we test numerically the results
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Gao, Xuefeng. "Stochastic models for service systems and limit order books." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/50238.
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Stochastic fluctuations can have profound impacts on engineered systems. Nonetheless, we can achieve significant benefits such as cost reduction based upon
expanding our fundamental knowledge of stochastic systems. The primary goal of this thesis is to contribute to our understanding by developing and analyzing stochastic models for specific types of engineered systems. The knowledge gained can help
management to optimize decision making under uncertainty.
This thesis has three parts. In Part I, we study many-server queues that model large-scale service systems such as call centers. We focus on the positive recurrence of
piecewise Ornstein-Uhlenbeck (OU) processes and the validity of using these processes to predict the steady-state performance of the corresponding many-server queues. In Part II, we investigate diffusion processes constrained to the positive orthant under infinitesimal changes in the drift.
This sensitivity analysis on the drift helps us understand how changes in service capacities at individual stations in a stochastic network would affect the steady-state queue-length distributions. In Part III, we
study the trading mechanism known as limit order book. We are motivated by a desire to better understand the interplay among order flow rates, liquidity fluctuation, and optimal executions. The goal is to characterize the temporal evolution of order
book shape on the “macroscopic” time scale.
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Song, Dongping. "Stochastic models in planning complex engineer-to-order products." Thesis, University of Newcastle Upon Tyne, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366477.
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Hu, Robert. "Optimal Order Execution using Stochastic Control and Reinforcement Learning." Thesis, KTH, Matematisk statistik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-192211.
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In this thesis an attempt is made to find the optimal order execution policy that maximizes the reward from trading financial instruments. The optimal policies are found us-ing a Markov Decision Process that is build using a state space model and the Bellman equation. Since there is not an explicit formula for state space dynamics, simulations on historical data are made instead to find the state transition probabilities and the rewards associated with each state and control. The optimal policy is then generated from the Bellman equation and tested against naive policies on out-of-sample data. This thesis also attempts to model the notion of market impact and test whether the Markov Deci-sion Process is still viable under the imposed assumptions. Lastly, there is also an attempt to estimate the value func-tion using various techniques from Reinforcement Learning. It turns out that naive strategies are superior when market impact is not present and when market impact is modeled as a direct penalty on reward. The Markov Decision Pro-cess is superior with market impact when it is modeled as having an impact on simulations, although some results suggest that the market impact model is not consistent for all types of instruments. Further, approximating the value function yields results that are inferior to the Markov Deci-sion Process, but interestingly the method exhibits an im-provement in performance if the estimated value function is trained before it is tested.I denna uppsats görs ett försök att hitta den optimala order exekverings strategi som maximerar vinsten från att handla finansiella instrument. Den optimala strategin hittas genom att använda en Markov beslutsprocess som är byggd på en tillståndsmodell och Bellman ekvationen. Eftersom det in-te finns en explicit formel för tillstånds dynamiken, görs istället simuleringar på historiska data för att uppskatta transitionssannolikheterna och vinsten associerad med var-je tillstånd och styrsignal. Den optimala strategin genereras sedan från Bellman ekvationen och testas mot naiva stra-tegier på test data. Det görs även ett försök att modellera marknads påverkan för att testa om Markov beslutsproces-ser fortfarande är gångbara under antagandena som görs. Slutligen görs även ett försök på att estimera värdesfunk-tionen med olika tekniker från ”Reinforcement Learning”. Det visar sig att naiva strategier är överlägsna när mark-nads påverkan inte inkorporeras och när marknads påver-kan modelleras som ett stra˙ på vinsten. Markov besluts-processer är överlägsna när marknads påverkan modelleras som direkta påverkningar på simuleringarna, men några av resultaten påvisar att modellen inte är konsistent för alla typer av instrument. Slutligen, så ger approximation av vär-desfunktionen sämre resultat än Markov beslutsprocesser, men intressant nog påvisar metoden en förbättring i pre-standa om den estimerade värdesfunktionen tränas innan den testas.
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Alhojilan, Yazid Yousef M. "Higher-order numerical scheme for solving stochastic differential equations." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/15973.
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We present a new pathwise approximation method for stochastic differential equations driven by Brownian motion which does not require simulation of the stochastic integrals. The method is developed to give Wasserstein bounds O(h3/2) and O(h2) which are better than the Euler and Milstein strong error rates O(√h) and O(h) respectively, where h is the step-size. It assumes nondegeneracy of the diffusion matrix. We have used the Taylor expansion but generate an approximation to the expansion as a whole rather than generating individual terms. We replace the iterated stochastic integrals in the method by random variables with the same moments conditional on the linear term. We use a version of perturbation method and a technique from optimal transport theory to find a coupling which gives a good approximation in Lp sense. This new method is a Runge-Kutta method or so-called derivative-free method. We have implemented this new method in MATLAB. The performance of the method has been studied for degenerate matrices. We have given the details of proof for order h3/2 and the outline of the proof for order h2.
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D'Souza, Raissa Michelle. "Macroscopic order from reversible and stochastic lattice growth models." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/16719.
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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 1999.Includes bibliographical references (p. 197-209).
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
This thesis advances the understanding of how autonomous microscopic physical processes give rise to macroscopic structure. A unifying theme is the use of physically motivated microscopic models of discrete systems which incorporate the constraints of locality, uniformity, and exact conservation laws. The features studied include: stochastic nonequilibrium fluctuations; use of pseudo-randomness in dynamical simulations; the thermodynamics of pattern formation; recurrence times of finite discrete systems; and computation in physical models. I focus primarily on pattern formation: transitions from a disordered to an ordered macroscopic state. Using an irreversible stochastic model of pattern formation in an open system driven by an external source of noise, I study thin film growth. I focus on the regimes of growth and the average properties of the resulting rough surfaces. I also show that this model couples sensitively to the imperfections of various pseudorandom number generators, resulting in non-stochastic exploration of the accessible state space. Using microscopically reversible models, I explicitly model how macroscopic dissipation can arise. In discrete systems with invertible dynamics entropy cannot decrease, and most such systems approach fully ergodic. Therefore these systems are natural candidates for models of thermodynamic behavior. I construct reversible models of pattern formation by dividing the system in two: the part of primary interest, and a "heat bath". We can observe the exchange of heat, energy, and entropy between the two subsystems, and gain insight into the thermodynamics of self-assembly. I introduce a local, deterministic, microscopically reversible model of cluster growth via aggregation in a closed two-dimensional system. The model has a realistic thermodynamics. When started from a state with low coarse grained entropy the model exhibits an initial regime of rapid nonequilibrium growth followed by a quasistatic regime with a well defined temperature. The growth clusters generated display a rich variety of morphologies. I also show how sequences of conditional aggregation events can be used to implement reusable logic gates and how to simulate any digital logic circuit with this model.
by Raissa Michelle D'Souza.
Ph.D.
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Liu, Liu. "Stochastic Optimization in Machine Learning." Thesis, The University of Sydney, 2019. http://hdl.handle.net/2123/19982.
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Stochastic optimization has received extensive attention in recent years due to their extremely potential for solving the large-scale optimization problem. However, the classical optimization algorithm and original stochastic method might prove to be inefficient due to the fact that: 1) the cost-per-iteration is a computational challenge, 2) the convergence and complexity are poorly performed. In this thesis, we exploit the stochastic optimization from three kinds of "order" optimization to address the problem. For the stochastic zero-order optimization, we introduce a novel variance reduction based method under Gaussian smoothing and establish the complexity for optimizing non-convex problems. With variance reduction on both sample space and search space, the complexity of our algorithm is sublinear to d and is strictly better than current approaches, in both smooth and non-smooth cases. Moreover, we extend the proposed method to the mini-batch version. For the stochastic first-order optimization, we consider two kinds of functions with one finite-sum and two finite-sums. The one first structure, we apply the dual coordinate ascent and accelerated algorithm to propose a general scheme for the double-accelerated stochastic method to deal with the ill-conditioned problem. The second structure, we apply the variance-reduced technique to derive the stochastic composition, including inner and outer finite-sum functions with a large number of component functions, via variance reduction that significantly improves the query complexity when the number of inner component functions is sufficiently large. For the stochastic second-order optimization, we study a family of stochastic trust region and cubic regularization methods when gradient, Hessian and function values are computed inexactly, and show the iteration complexity to achieve $\epsilon$-approximate second-order optimality is in the same order with previous work for which gradient and function values are computed exactly. The mild conditions on inexactness can be achieved in finite-sum minimization using random sampling.
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Rodríguez, Cruz Yolanda Rocío [Verfasser]. "Model Order Reduction for Stochastic Systems / Yolanda Rocío Rodríguez Cruz." München : Verlag Dr. Hut, 2018. http://d-nb.info/1162767596/34.
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Alnafisah, Yousef Ali. "First-order numerical schemes for stochastic differential equations using coupling." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20420.
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We study a new method for the strong approximate solution of stochastic differential equations using coupling and we prove order one error bounds for the new scheme in Lp space assuming the invertibility of the diffusion matrix. We introduce and implement two couplings called the exact and approximate coupling for this scheme obtaining good agreement with the theoretical bound. Also we describe a method for non-invertibility case (Combined method) and we investigate its convergence order which will give O(h3/4 √log(h)j) under some conditions. Moreover we compare the computational results for the combined method with its theoretical error bound and we have obtained a good agreement between them. In the last part of this thesis we work out the performance of the multilevel Monte Carlo method using the new scheme with the exact coupling and we compare the results with the trivial coupling for the same scheme.
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Honeycutt, Rebecca Lee. "Higher order algorithms for the numerical integration of stochastic differential equations." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/29907.
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Niezgoda, Stephen Richard Kalidindi Surya. "Stochastic representation of microstructure via higher-order statistics : theory and application /." Philadelphia, Pa. : Drexel University, 2010. http://hdl.handle.net/1860/3320.
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Fruth, Antje [Verfasser], and Peter [Akademischer Betreuer] Bank. "Optimal order execution with stochastic liquidity / Antje Fruth. Betreuer: Peter Bank." Berlin : Universitätsbibliothek der Technischen Universität Berlin, 2011. http://d-nb.info/1014946697/34.
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Zhou, Chao. "Model Uncertainty in Finance and Second Order Backward Stochastic Differential Equations." Palaiseau, Ecole polytechnique, 2012. https://pastel.hal.science/docs/00/77/14/37/PDF/Thesis_ZHOU_Chao_Pastel.pdfcc.
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L'objectif principal de cette thèse est d'étudier quelques problèmes de mathématiques financières dans un marché incomplet avec incertitude sur les modèles. Récemment, la théorie des équations différentielles stochastiques rétrogrades du second ordre (2EDSRs) a été développée par Soner, Touzi et Zhang sur ce sujet. Dans cette thèse, nous adoptons leur point de vue. Cette thèse contient quatre parties dans le domain des 2EDSRs. Nous commençons par généraliser la théorie des 2EDSRs initialement introduite dans le cas de générateurs lipschitziens continus à celui de générateurs à croissance quadratique. Cette nouvelle classe des 2EDSRs nous permettra ensuite d'étudier le problème de maximisation d'utilité robuste dans les modèles non-dominés. Dans la deuxième partie, nous étudions ce problème pour trois fonctions d'utilité. Dans chaque cas, nous donnons une caractérisation de la fonction valeur et d'une stratégie d'investissement optimale via la solution d'une 2EDSR. Dans la troisième partie, nous fournissons également une théorie d'existence et unicité pour des EDSRs réfléchies du second ordre avec obstacles inférieurs et générateurs lipschitziens, nous appliquons ensuite ce résultat à l'étude du problème de valorisation des options américaines dans un modèle financier à volatilité incertaine. Dans la quatrième partie, nous étudions des 2EDSRs avec sauts. En particulier, nous prouvons l'existence d'une unique solution dans un espace approprié. Comme application de ces résultats, nous étudions un problème de maximisation d'utilité exponentielle robuste avec incertitude sur les modèles. L'incertitude affecte à la fois le processus de volatilité, mais également la mesure des sautsThe main objective of this PhD thesis is to study some financial mathematics problems in an incomplete market with model uncertainty. In recent years, the theory of second order backward stochastic differential equations (2BSDEs for short) has been developed by Soner, Touzi and Zhang on this topic. In this thesis, we adopt their point of view. This thesis contains of four key parts related to 2BSDEs. In the first part, we generalize the 2BSDEs theory initially introduced in the case of Lipschitz continuous generators to quadratic growth generators. This new class of 2BSDEs will then allow us to consider the robust utility maximization problem in non-dominated models. In the second part, we study this problem for exponential utility, power utility and logarithmic utility. In each case, we give a characterization of the value function and an optimal investment strategy via the solution to a 2BSDE. In the third part, we provide an existence and uniqueness result for second order reflected BSDEs with lower obstacles and Lipschitz generators, and then we apply this result to study the problem of American contingent claims pricing with uncertain volatility. In the fourth part, we define a notion of 2BSDEs with jumps, for which we prove the existence and uniqueness of solutions in appropriate spaces. We can interpret these equations as standard BSDEs with jumps, under both volatility and jump measure uncertainty. As an application of these results, we shall study a robust exponential utility maximization problem under model uncertainty, where the uncertainty affects both the volatility process and the jump measure
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Huang, Huiting. "Permutation tests for stochastic ordering with ordered categorical data." Doctoral thesis, Università degli studi di Padova, 2019. http://hdl.handle.net/11577/3423299.
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Ordered categorical data are frequently encountered in many fields of research, such as, sociology, psychology, quality control, medical studies, and so forth. Especially in medical research, it is inevitable to meet a lot of problems containing ordered categorical data. Our specific interest is to find convincing solutions to some of the testing problems which include restrictions in the set of alternatives, such as testing for stochastic dominance and testing for monotonic stochastic ordering while using such a kind of data. When the number of nuisance parameters of underlying distributions or that of observed variables is small, there are some likelihood-based solutions. Our interest, however, is for cases where such numbers are not small. In these cases likelihood-based methods do not work, thus our interest is to proceed nonparametrically within permutation methods. Permutation methods are conditional on the pooled set of observed data which, in turn, are typically a set of sufficient statistics under the null hypothesis for the underlying distribution. Moreover, due to the evident complexity of such problems, according to Roy (1953), we also must use their Union-Intersection representation consisting on an equivalent break-down of the hypothesis under testing into a set of simpler sub-hypotheses for each of which a permutation test is available and such tests are jointly considered. So we must stay within the nonparametric combination of several dependent permutation tests. In the thesis, guided by two medical examples from the literature, we propose suitable solutions that are proved to be admissible combinations of optimal conditional partial tests and so enjoying good asymptotic properties.
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Cheng, Jianqiang. "Stochastic Combinatorial Optimization." Thesis, Paris 11, 2013. http://www.theses.fr/2013PA112261.
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Dans cette thèse, nous étudions trois types de problèmes stochastiques : les problèmes avec contraintes probabilistes, les problèmes distributionnellement robustes et les problèmes avec recours. Les difficultés des problèmes stochastiques sont essentiellement liées aux problèmes de convexité du domaine des solutions, et du calcul de l’espérance mathématique ou des probabilités qui nécessitent le calcul complexe d’intégrales multiples. A cause de ces difficultés majeures, nous avons résolu les problèmes étudiées à l’aide d’approximations efficaces.Nous avons étudié deux types de problèmes stochastiques avec des contraintes en probabilités, i.e., les problèmes linéaires avec contraintes en probabilité jointes (LLPC) et les problèmes de maximisation de probabilités (MPP). Dans les deux cas, nous avons supposé que les variables aléatoires sont normalement distribués et les vecteurs lignes des matrices aléatoires sont indépendants. Nous avons résolu LLPC, qui est un problème généralement non convexe, à l’aide de deux approximations basée sur les problèmes coniques de second ordre (SOCP). Sous certaines hypothèses faibles, les solutions optimales des deux SOCP sont respectivement les bornes inférieures et supérieures du problème du départ. En ce qui concerne MPP, nous avons étudié une variante du problème du plus court chemin stochastique contraint (SRCSP) qui consiste à maximiser la probabilité de la contrainte de ressources. Pour résoudre ce problème, nous avons proposé un algorithme de Branch and Bound pour calculer la solution optimale. Comme la relaxation linéaire n’est pas convexe, nous avons proposé une approximation convexe efficace. Nous avons par la suite testé nos algorithmes pour tous les problèmes étudiés sur des instances aléatoires. Pour LLPC, notre approche est plus performante que celles de Bonferroni et de Jaganathan. Pour MPP, nos résultats numériques montrent que notre approche est là encore plus performante que l’approximation des contraintes probabilistes individuellement.La deuxième famille de problèmes étudiés est celle relative aux problèmes distributionnellement robustes où une partie seulement de l’information sur les variables aléatoires est connue à savoir les deux premiers moments. Nous avons montré que le problème de sac à dos stochastique (SKP) est un problème semi-défini positif (SDP) après relaxation SDP des contraintes binaires. Bien que ce résultat ne puisse être étendu au cas du problème multi-sac-à-dos (MKP), nous avons proposé deux approximations qui permettent d’obtenir des bornes de bonne qualité pour la plupart des instances testées. Nos résultats numériques montrent que nos approximations sont là encore plus performantes que celles basées sur les inégalités de Bonferroni et celles plus récentes de Zymler. Ces résultats ont aussi montré la robustesse des solutions obtenues face aux fluctuations des distributions de probabilités. Nous avons aussi étudié une variante du problème du plus court chemin stochastique. Nous avons prouvé que ce problème peut se ramener au problème de plus court chemin déterministe sous certaine hypothèses. Pour résoudre ce problème, nous avons proposé une méthode de B&B où les bornes inférieures sont calculées à l’aide de la méthode du gradient projeté stochastique. Des résultats numériques ont montré l’efficacité de notre approche. Enfin, l’ensemble des méthodes que nous avons proposées dans cette thèse peuvent s’appliquer à une large famille de problèmes d’optimisation stochastique avec variables entièresIn this thesis, we studied three types of stochastic problems: chance constrained problems, distributionally robust problems as well as the simple recourse problems. For the stochastic programming problems, there are two main difficulties. One is that feasible sets of stochastic problems is not convex in general. The other main challenge arises from the need to calculate conditional expectation or probability both of which are involving multi-dimensional integrations. Due to the two major difficulties, for all three studied problems, we solved them with approximation approaches.We first study two types of chance constrained problems: linear program with joint chance constraints problem (LPPC) as well as maximum probability problem (MPP). For both problems, we assume that the random matrix is normally distributed and its vector rows are independent. We first dealt with LPPC which is generally not convex. We approximate it with two second-order cone programming (SOCP) problems. Furthermore under mild conditions, the optimal values of the two SOCP problems are a lower and upper bounds of the original problem respectively. For the second problem, we studied a variant of stochastic resource constrained shortest path problem (called SRCSP for short), which is to maximize probability of resource constraints. To solve the problem, we proposed to use a branch-and-bound framework to come up with the optimal solution. As its corresponding linear relaxation is generally not convex, we give a convex approximation. Finally, numerical tests on the random instances were conducted for both problems. With respect to LPPC, the numerical results showed that the approach we proposed outperforms Bonferroni and Jagannathan approximations. While for the MPP, the numerical results on generated instances substantiated that the convex approximation outperforms the individual approximation method.Then we study a distributionally robust stochastic quadratic knapsack problems, where we only know part of information about the random variables, such as its first and second moments. We proved that the single knapsack problem (SKP) is a semedefinite problem (SDP) after applying the SDP relaxation scheme to the binary constraints. Despite the fact that it is not the case for the multidimensional knapsack problem (MKP), two good approximations of the relaxed version of the problem are provided which obtain upper and lower bounds that appear numerically close to each other for a range of problem instances. Our numerical experiments also indicated that our proposed lower bounding approximation outperforms the approximations that are based on Bonferroni's inequality and the work by Zymler et al.. Besides, an extensive set of experiments were conducted to illustrate how the conservativeness of the robust solutions does pay off in terms of ensuring the chance constraint is satisfied (or nearly satisfied) under a wide range of distribution fluctuations. Moreover, our approach can be applied to a large number of stochastic optimization problems with binary variables.Finally, a stochastic version of the shortest path problem is studied. We proved that in some cases the stochastic shortest path problem can be greatly simplified by reformulating it as the classic shortest path problem, which can be solved in polynomial time. To solve the general problem, we proposed to use a branch-and-bound framework to search the set of feasible paths. Lower bounds are obtained by solving the corresponding linear relaxation which in turn is done using a Stochastic Projected Gradient algorithm involving an active set method. Meanwhile, numerical examples were conducted to illustrate the effectiveness of the obtained algorithm. Concerning the resolution of the continuous relaxation, our Stochastic Projected Gradient algorithm clearly outperforms Matlab optimization toolbox on large graphs
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Ait, El Faqir Marouane. "Prédiction de la structure de contrôle de bactéries par optimisation sous incertitude." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEC036/document.
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L'approche de la biologie des systèmes vise à intégrer les méthodologies appliquées dans la conception et l'analyse des systèmes technologiques complexes, au sein de la biologie afin de comprendre les principes de fonctionnement globaux des systèmes biologiques. La thèse s'inscrit dans le cadre de la biologie des systèmes et en particulier dans la prolongation d'une méthode issue de ce cadre : la méthode Resource Blance Analysis (RBA). Nous visons dans cette thèse à augmenter le pouvoir prédictif de la méthode via un travail de modélisation tout en gardant un bon compromis entre représentativité des modèles issus de ce cadre et leur résolution numérique efficace. La thèse se décompose en deux grandes parties : la première vise à intégrer les aspects thermodynamiques et cinétiques inhérents aux réseaux métaboliques. La deuxième vise à comprendre l'impact de l'aspect stochastique de la production des enzymes sur le croissance de la bactérie. Des méthodes numériques ont été élaborées pour la résolution des modèles ainsi établis dans les deux cas déterministe et stochastiqueIn order to understand the global functioning principals of biological systems, system bio- logy approach aims to integrate the methodologies used in the conception and the analysis of complex technological systems, within the biology. This PhD thesis fits into the system biology framework and in particular the extension of the already existing method Resource Balance Analysis (RBA). We aim in this PhD thesis to improve the predictive power of this method by introducing more complex model. However, this new model should respect a good trade-off between the representativity of the model and its efficient numerical computation. This PhD thesis is decomposed into two major parts. The first part aims the integration of the metabolic network inherent thermodynamical and kinetic aspects. The second part aims the comprehension of the impact of enzyme production stochastic aspect on the bacteria growth. Numerical methods are elaborated to solve the obtained models in both deterministic and stochastic cases
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Herath, Narmada Kumari. "Model order reduction for stochastic models of biomolecular systems with time-scale separation." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/118083.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 177-183).
Biomolecular systems often involve reactions that take place on different time-scales, giving rise to 'slow' and 'fast' system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In deterministic systems, methods to obtain such reduced-order models are well defined by the singular perturbation or averaging techniques. However, model reduction of stochastic systems remains an ongoing area of research. In particular, existing model reduction methods for stochastic models of biomolecular systems lack rigorous error quantifications between the full and reduced dynamics. Furthermore, they only provide approximations for the slow variable dynamics, making the application of such methods to biomolecular systems difficult since the variables of interest are typically mixed (i.e., they encompass both fast and slow variables). In this thesis, we consider biomolecular systems modeled using the chemical Langevin equation (CLE) and the Linear Noise Approximation (LNA). Specifically, we consider biomolecular systems with linear propensity functions modeled by the CLE and systems with arbitrary propensity functions modeled by the LNA. For these systems, we obtain reduced-order models that approximate both the slow and fast variables under time-scale separation conditions. In particular, with suitable assumptions, we prove that the moments of the reduced-order models converge to those of the full systems as the time-scale separation becomes large. Our results further provide a rigorous justification for the accuracy of the stochastic total quasi-steady state approximation (tQSSA). We then consider two applications of these reduced-order models. In the first application, we analyze the trade-offs between modularity and signal noise in biomolecular networks. In the second application, we consider the application of the reduced-order LNA developed in this work to obtain reduced-order stochastic models for gene-regulatory networks.
by Narmada Kumari Herath.
Ph. D.
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Borrello, Davide. "Interacting particle systems : stochastic order, attractiveness and random walk on small world grahs." Rouen, 2009. http://www.theses.fr/2009ROUES032.
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Le sujet principal de la thèse sont les systèmes de particules en interaction, qui sont des classes de processus spatio-temporels. Ces systèmes décrivent l'évolution de particules en interaction les unes avec les autres sur un espace discret fini ou infini. Dans la partie I, nous examinons l'ordre stochastique dans un système de particules avec multiples naissances, morts et sauts sur l'espace d-dimensionnel à coordonnées entières. Nous donnons des applications pour des modèles biologiques de diffusion d'épidémies et de systèmes de dynamiques de métapopulations. Dans la partie II, nous analysons la marche aléatoire coalescente dans une classe de graphes aléatoires finis qui modèlent les réseaux sociaux, les graphes "small word"The main subject of the thesis is concerned with interacting particle systems, which are classes of spatio-temporal stochastic processes describing the evolution of particles in interaction with each other on a finite or infinite discrete space. In part I we investigate the stochastic order in a particle system with multiple births, deaths and jumps on the d-dimensional lattice. We give applications on biological models of spread of epidemics and metapopulations dynamics systems. In part II we analyse the coalescing random walk in a class of finite random graphs modeling social networks, the small world graphs
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Silveti, Falls Antonio. "First-order noneuclidean splitting methods for large-scale optimization : deterministic and stochastic algorithms." Thesis, Normandie, 2021. http://www.theses.fr/2021NORMC204.
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Dans ce travail, nous développons et examinons deux nouveaux algorithmes d'éclatement du premier ordre pour résoudre des problèmes d'optimisation composites à grande échelle dans des espaces à dimensions infinies. Ces problèmes sont au coeur de nombres de domaines scientifiques et d'ingénierie, en particulier la science des données et l'imagerie. Notre travail est axé sur l'assouplissement des hypothèses de régularité de Lipschitz généralement requises par les algorithmes de fractionnement du premier ordre en remplaçant l'énergie euclidienne par une divergence de Bregman. Ces développements permettent de résoudre des problèmes ayant une géométrie plus exotique que celle du cadre euclidien habituel. Un des algorithmes développés est l'hybridation de l'algorithme de gradient conditionnel, utilisant un oracle de minimisation linéaire à chaque itération, avec méthode du Lagrangien augmenté, permettant ainsi la prise en compte de contraintes affines. L'autre algorithme est un schéma d'éclatement primal-dual incorporant les divergences de Bregman pour le calcul des opérateurs proximaux associés. Pour ces deux algorithmes, nous montrons la convergence des valeurs Lagrangiennes, la convergence faible des itérés vers les solutions ainsi que les taux de convergence. En plus de ces nouveaux algorithmes déterministes, nous introduisons et étudions également leurs extensions stochastiques au travers d'un point de vue d'analyse de stablité aux perturbations. Nos résultats dans cette partie comprennent des résultats de convergence presque sûre pour les mêmes quantités que dans le cadre déterministe, avec des taux de convergence également. Enfin, nous abordons de nouveaux problèmes qui ne sont accessibles qu'à travers les hypothèses relâchées que nos algorithmes permettent. Nous démontrons l'efficacité numérique et illustrons nos résultats théoriques sur des problèmes comme la complétion de matrice parcimonieuse de rang faible, les problèmes inverses sur le simplexe, ou encore les problèmes inverses impliquant la distance de Wasserstein régulariséeIn this work we develop and examine two novel first-order splitting algorithms for solving large-scale composite optimization problems in infinite-dimensional spaces. Such problems are ubiquitous in many areas of science and engineering, particularly in data science and imaging sciences. Our work is focused on relaxing the Lipschitz-smoothness assumptions generally required by first-order splitting algorithms by replacing the Euclidean energy with a Bregman divergence. These developments allow one to solve problems having more exotic geometry than that of the usual Euclidean setting. One algorithm is hybridization of the conditional gradient algorithm, making use of a linear minimization oracle at each iteration, with an augmented Lagrangian algorithm, allowing for affine constraints. The other algorithm is a primal-dual splitting algorithm incorporating Bregman divergences for computing the associated proximal operators. For both of these algorithms, our analysis shows convergence of the Lagrangian values, subsequential weak convergence of the iterates to solutions, and rates of convergence. In addition to these novel deterministic algorithms, we introduce and study also the stochastic extensions of these algorithms through a perturbation perspective. Our results in this part include almost sure convergence results for all the same quantities as in the deterministic setting, with rates as well. Finally, we tackle new problems that are only accessible through the relaxed assumptions our algorithms allow. We demonstrate numerical efficiency and verify our theoretical results on problems like low rank, sparse matrix completion, inverse problems on the simplex, and entropically regularized Wasserstein inverse problems
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Ali, Naseem Kamil. "Thermally (Un-) Stratified Wind Plants: Stochastic and Data-Driven Reduced Order Descriptions/Modeling." PDXScholar, 2018. https://pdxscholar.library.pdx.edu/open_access_etds/4634.
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Wind energy is one of the significant sources of renewable energy, yet a number of challenges preclude optimal operation of wind plants. Research is warranted in order to minimize the power losses and improve the productivity of wind plants. Here, a framework combining turbulence theory and data mining techniques is built to elucidate physics and mechanisms driving the energy extraction of the wind plants under a number of atmospheric/operating conditions. The performance of wind turbines is subjected to adverse effects caused by wake interactions. Therefore, it is crucial to understand wake-to-wake interactions as well as wake-to-atmospheric boundary layer interactions. Experimental and numerical data sets are examined in order to provide descriptions of the wakes and extract relevant features. As wakes merge, it is of interest to observe characteristics within the turbulent velocity signal obtained via wind tunnel experiments. Higher order moments, structure functions, intermittency and multifractality analysis are investigated to distinguish the flow dynamics. In this manner, considered approaches highlight the flow deceleration induced by the wind turbines, which subsequently changes the energy transfer rate imposed by the coherent eddies, and adapt the equilibrium range in the energy cascade. Also, wind turbines induce scale interactions and cause the intermittency that lingers at large and small scales. When wind plants interact dynamically with small scales, the flow becomes highly intermittent and multifractality is increased, especially near the rotor. Multifractality parameters, including the Hurst exponent and the combination factor, show the ability to describe the flow state in terms of its development. Based on Markov theory, the time evolution of the probability density function of the velocity is described via the Fokker-Planck equation and its Kramers-Moyal coefficients. Stochastic analysis proves the non-universality of the turbulent cascade immediate to the rotor, and the impact of the generation mechanism on flow cascade. Classifying the wake flow based the velocity and intermittency signs emphasizes that a negative correlation is dominant downstream from the rotor. These results reflect large-scale organization of the velocity-intermittency events corresponding to a recirculation region near the hub height and bottom tip. A linear regression approach based on the Gram-Charlier series expansion of the joint probability density function successfully models the contribution of the second and fourth quadrants. Thus, the model is able to predict the imbalance in the velocity and intermittency contribution to momentum transfer. Via large eddy simulations, the structure of the turbulent flow within the array under stratified conditions is quantified through the use of the Reynolds stress anisotropy tensor, proper orthogonal decomposition and cluster-based modeling. Perturbations induced by the turbine wakes are absorbed by the background turbulence in the unstable and neutrally stratified cases. Contrary, the flow in the stable stratified case is fully dominated by the presence of turbines and extremely influenced by the Coriolis force. Also, during the unstable period the turbulent kinetic energy is maximum. Thus, leading to fast convergence of the cumulative energy with only few modes. Reynolds stress anisotropy tensor reveals that under unstable thermal stratification the turbulence state tends to be more isotropic. The turbulent mixing due to buoyancy determines the degree of anisotropy and the energy distribution between the flow layers. The wakes of the turbines display large degree of anisotropy due to the correlation with the turbulent kinetic energy production. A combinatorial technique merging image segmentation via K-Means clustering and colormap of the barycentric map is posed. Clustering aids in extracting identical features from the spatial distribution of anisotropy colormap images by minimizing the sum of squared error over all clusters. Clustering also enables to highlight the wake expansion and interaction as produced by the wind turbines as a function of thermal stratification. A cluster-based reduced-order dynamical model is proposed for flow field and passive scalars; the model relies on full-state measurements. The dynamical behavior is predicted through the cluster transition matrix and modeled as a Markov process. The geometric nature of the attractor shows the ability to assess the quality of the clustering and identify transition regions. Periodical trends in the cluster transition matrix characterize the intrinsic periodical behavior of the wake. The modeling strategy points out a feasible path for future design and control that can be used to maximize power output. In addition, characterization of intermittency with power integration model can allow for power fluctuation arrangement/prediction in wind plants.
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BORRELLO, DAVIDE. "Interacting particle systems: stochastic order, attractiveness and random walks on small world graphs." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2009. http://hdl.handle.net/10281/7467.
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The main subject of the thesis is concerned with interacting particle systems, which are
classes of spatio-temporal stochastic processes describing the evolution of particles in interaction with each other.
The particles move on a finite or infinite discrete space and on each element of this space the state of the configuration is integer valued. Configurations of particles evolve in continuous
time according to a Markov process. Here the space is either the infinite deterministic
d-dimensional lattice or a random graph given by the finite d-dimensional torus with random matchings. In Part I we investigate the stochastic order in a particle system with multiple births, deaths and jumps on the d-dimensional lattice: stochastic order is a key tool to understand the ergodic properties of a system. We give applications on biological models of spread of epidemics and metapopulation dynamics systems. In Part II we analyse the coalescing random walk in a class of finite random graphs modeling social networks, the small world graphs. We derive the law of the meeting time of two random walks on small world graphs and we use this result to understand the role
of random connections in meeting time of random walks and to investigate the behavior
of coalescing random walks.
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Almazmomi, Afnan. "Likelihood Inference for Order Restricted Models." Digital WPI, 2018. https://digitalcommons.wpi.edu/etd-theses/355.
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As we know the most popular inference methods for order restricted model are likelihood inference. In such models, the Maximum Likelihood Estimation (MLE) and Likelihood Ratio Testing (LRT) appear some suspect behaviour and unsatisfactory. In this thesis, I review the articles that focused in the behaviour of the Likelihood methods on Order restricted models. For those situations, an alternative method is preferred. However, likelihood inference is satisfactory for simple order cone restriction. But it is unsatisfactory when the restrictions are of the tree order, umbrella order, star-shaped and stochastic order types.
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Chabot, John Alva. "VALIDATING STEADY TURBULENT FLOW SIMULATIONS USING STOCHASTIC MODELS." Miami University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=miami1443188391.
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Talukdar, Saifulla. "Ekofisk Chalk: Core Measurements, Stochastic Reconstruction, Network Modeling and Simulation." Doctoral thesis, Norwegian University of Science and Technology, Faculty of Engineering Science and Technology, 2002. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-120.
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This dissertation deals with (1) experimental measurements on petrophysical reservoir engineering and morphological properties of Ekofisk chalk, (2) numerical simulation of core flood experiments to analyze and improve relative permeability data, (3) stochastic reconstruction of chalk samples from limited morphological information, (4) extraction of pore space parameters from the reconstructed samples, development of network model using pore space information, and computation of petrophysical and reservoir engineering properties from network model, and (5) development of 2D and 3D idealized fractured reservoir models and verification of the applicability of several widely used conventional upscaling techniques in fractured reservoir simulation.
Experiments have been conducted on eight Ekofisk chalk samples and porosity, absolute permeability, formation factor, and oil-water relative permeability, capillary pressure and resistivity index are measured at laboratory conditions. Mercury porosimetry data and backscatter scanning electron microscope images have also been acquired for the samples.
A numerical simulation technique involving history matching of the production profits is employed to improve the relative permeability curves and to analyze hysteresis of the Ekofisk chalk sample. The technique was found to be a powerful tool to supplement the uncertainties in experimental measurements.
Porosity and correlation statistics obtained from backscatter scanning electron microscope image are used to reconstruct microstructures of chalk and particulate media. The reconstruction technique involves a simulated annealing algorithm, which can be constrained by an arbitrary number of morphological parameters. This flexibility of the algorithm is exploited to successfully reconstruct particulate media and chalk samples using more that one correlation function. A technique based on conditional simulated annealing has been introduced for exact reproduction of vuggy porosity in chalk in the form of foraminifer shells. A hybrid reconstruction technique that initialized the simulated annealing reconstruction with input generated using the Gaussian random field model has also been introduced. The technique was found to accelerate significantly the rate of convergence of the simulated annealing method. This finding is important because the main advantage of the simulated annealing method, namely its ability to impose a variety of reconstruction constraints, is usually compromised by its very slow rate of convergence.
Absolutely permeability, formation factor and mercury-air capillary pressure are computed from simple network models. The input parameters for the network models were extracted from a reconstructed chalk sample. The computed permeability, formation factor and mercury-air capillary pressure correspond well with the experimental data. The predictive power of a network model for chalk is further extended through incorporating important pore-level displacement phenomena and realistic description of pore space geometry and topology. Limited results show that the model may be used to compute absolute and relative permeabilities, capillary pressure, formation factor, resistivity index and saturation exponent. The above findings suggest that the network modeling technique may be used for prediction of petrophysical and reservoir engineering properties of chalk. Further works are necessary and an outline is given with considerable details.
Two 2D, one 3D and a dual-porosity fractured reservoir models have been developed and an imbibition process involving water displacing oil is simulated at various injection rates and with different oil-to-water viscosity ratios using four widely used conventional upscaling techniques. The upscaling techniques are the Kyte & Berry, Pore Volume Weighted, Weighed Relative Permeability, and Stone. The results suggest that the upscaling of fractured reservoirs may be possible using the conventional techniques. Kyte & Berry technique was found to be the most effective in all situations. However, further investigations are necessary using realistic description of fracture length, orientation, connectivity, aperture, spacing, etc.
Paper 3,4 and 5 reprinted with kind persmission of Elsevier Science, Science Direct.
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Blair, James. "Modelling approaches for optimal liquidation under a limit-order book structure." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/modelling-approaches-for-optimal-liquidation-under-a-limitorder-book-structure(a7c23b2a-e2f8-4b4a-9865-8783d9837198).html.
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This thesis introduces a selection of models for optimal execution of financial assets at the tactical level. As opposed to optimal scheduling, which defines a trading schedule for the trader, this thesis investigates how the trader should interact with the order book. If a trader is aggressive he will execute his order using market orders, which will negatively feedback on his execution price through market impact. Alternatively, the models we focus on consider a passive trader who places limit orders into the limit-order book and waits for these orders to be filled by market orders from other traders. We assume these models do not exhibit market impact. However, given we await market orders from other participants to fill our limit orders a new risk is borne: execution risk. We begin with an extension of Guéant et al. (2012b) who through the use of an exponential utility, standard Brownian motion, and an absolute decay parameter were able to cleverly build symmetry into their model which significantly reduced the complexity. Our model consists of geometric Brownian motion (and mean-reverting processes) for the asset price, a proportional control parameter (the additional amount we ask for the asset), and a proportional decay parameter, implying that the symmetry found in Guéant et al. (2012b) no longer exists. This novel combination results in asset-dependent trading strategies, which to our knowledge is a unique concept in this framework of literature. Detailed asymptotic analyses, coupled with advanced numerical techniques (informing the asymptotics) are exploited to extract the relevant dynamics, before looking at further extensions using similar methods. We examine our above mentioned framework, as well as that of Guéant et al. (2012), for a trader who has a basket of correlated assets to liquidate. This leads to a higher-dimensional model which increases the complexity of both numerically solving the problem and asymptotically examining it. The solutions we present are of interest, and comparable with Markowitz portfolio theory. We return to our framework of a single underlying and consider four extensions: a stochastic volatility model which results in an added dimension to the problem, a constrained optimisation problem in which the control has an explicit lower bound, changing the exponential intensity to a power intensity which results in a reformulation as a singular stochastic control problem, and allowing the trader to trade using both market orders and limit orders resulting in a free-boundary problem. We complete the study with an empirical analysis using limit-order book data which contains multiple levels of the book. This involves a novel calibration of the intensity functions which represent the limit-order book, before backtesting and analysing the performance of the strategies.
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Adnane, Alaoui M'Hamdi. "Modelling and analysis of consumer's multi-decision process : a new integrated stochastic modelling framework." Thesis, University of Edinburgh, 2012. http://hdl.handle.net/1842/9415.
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Interest in understanding Human Beings’ behaviour can be traced back to the early days of mankind. However, interest in consumer behaviour is relatively recent. In fact, it is only since the end of World War II and following economic prosperity of some nations (e.g., U.S.A.) that the world witnessed the rise of a new discipline in the early 1950s; namely, Marketing Research. By the end of the 1950s, academic papers on modelling and analysis of consumer behaviour started to appear (Ehrenberg, 1959; Frank, 1962). The purpose of this research is to propose an integrated decision framework for modelling consumer behaviour with respect to store incidence, category incidence, brand incidence, and size incidence. To the best of our knowledge, no published contribution integrates these decisions within the same modelling framework. In addition, the thesis proposes a new estimation method as well as a new segmentation method. These contributions aim at improving our understanding of consumer behaviour before and during consumers’ visits to the retail points of a distribution network, improving consumer behaviour prediction accuracy, and assisting with inventory management across distribution networks. The proposed modelling framework is hybrid in nature in that it uses both non-explanatory and explanatory models. To be more specific, it uses stochastic models; namely, probability distributions, to capture the intrinsic nature of consumers (i.e., inner or built-in behavioural features) as well as any unexplained similarities or differences (i.e., unobserved heterogeneity) in their intrinsic behaviour. In addition, the parameters of these probability distribution models could be estimated using explanatory models; namely, multiple regression models, such as logistic regression. Furthermore, the thesis proposes a piece-wise estimation procedure for estimating the parameters of the developed stochastic models. Also proposed is a three-step segmentation method based on the information provided by the quality of fit of stochastic models to consumer data so as to identify which model better predicts which market segments. In the empirical investigation, the proposed framework was used to study consumer behaviour with respect to individual alternatives of each decision, individual decisions, and all decisions. In addition, the proposed segmentation method was used to segment the panellists into infrequent users, light to medium users, and heavy users, on one hand, and split loyals, loyals, and hardcore loyals, on the other hand. Furthermore, the empirical evidence suggests that the proposed piece-wise estimation procedure outperforms the standard approach for all models and decision levels. Also, the empirical results revealed that the homogeneous MNL outperforms both the heterogeneous NMNL and DMNL when each one of these distributions is applied to all decisions, which suggests the relative homogeneity in consumer decision making at the aggregate or integrated decision level. Last, but not least, through the use of the proposed framework, the thesis sheds light on the importance of consumer choice sequence on the quality of predictions, which affects the quality of segmentation. The reader is referred to chapter 3 for details on these contributions.
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Pefferly, Robert J. "Finite difference approximations of second order quasi-linear elliptic and hyperbolic stochastic partial differential equations." Thesis, University of Edinburgh, 2001. http://hdl.handle.net/1842/11244.
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This thesis covers topics such as finite difference schemes, mean-square convergence, modelling, and numerical approximations of second order quasi-linear stochastic partial differential equations (SPDE) driven by white noise in less than three space dimensions. The motivation for discussing and expanding these topics lies in their implications in such physical phenomena as signal and information flow, gravitational and electromagnetic fields, large scale weather systems, and macro-computer networks. Chapter 2 delves into the hyperbolic SPDE in one space and one time dimension. This is an important equation to such fields as signal processing, communications, and information theory where singularities propagate throughout space as a function of time. Chapter 3 discusses some concepts and implications of elliptic SPDE's driven by additive noise. These systems are key for understanding steady state phenomena. Chapter 4 presents some numerical work regarding elliptic SPDE's driven by multiplicative and general noise. These SPDE's are open topics in the theoretical literature, hence numerical work provides significant insight into the nature of the process. Chapter 5 presents some numerical work regarding quasi-geostrophic geophysical fluid dynamics involving stochastic noise and demonstrates how these systems can be represented as a combination of elliptic and hyperbolic components.
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Goodson, Justin Christopher. "Solution methodologies for vehicle routing problems with stochastic demand." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/675.
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We present solution methodologies for vehicle routing problems (VRPs) with stochastic demand, with a specific focus on the vehicle routing problem with stochastic demand (VRPSD) and the vehicle routing problem with stochastic demand and duration limits (VRPSDL). The VRPSD and the VRPSDL are fundamental problems underlying many operational challenges in the fields of logistics and supply chain management.
We model the VRPSD and the VRPSDL as large-scale Markov decision processes. We develop cyclic-order neighborhoods, a general methodology for solving a broad class of VRPs, and use this technique to obtain static, fixed route policies for the VRPSD. We develop pre-decision, post-decision, and hybrid rollout policies for approximate dynamic programming (ADP). These policies lay a methodological foundation for solving large-scale sequential decision problems and provide a framework for developing dynamic routing policies.
Our dynamic rollout policies for the VRPSDL significantly improve upon a method frequently implemented in practice. We also identify circumstances in which our rollout policies appear to offer little or no benefit compared to this benchmark. These observations can guide managerial decision making regarding when the use of our procedures is justifiable. We also demonstrate that our methodology lends itself to real-time implementation, thereby providing a mechanism to make high-quality, dynamic routing decisions for large-scale operations.
Finally, we consider a more traditional ADP approach to the VRPSDL by developing a parameterized linear function to approximate the value functions corresponding to our problem formulation. We estimate parameters via a simulation-based algorithm and show that initializing parameter values via our rollout policies leads to significant improvements. However, we conclude that additional research is required to develop a parametric ADP methodology comparable or superior to our rollout policies.
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Moreira, Lucas 1984. "Processos de ordem infinita estocasticamente perturbados." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306189.
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Orientador: Nancy Lopes GarciaTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-19T13:37:17Z (GMT). No. of bitstreams: 1 Moreira_Lucas_D.pdf: 778475 bytes, checksum: 78934b9baf39cc234f800623a7af5cdf (MD5) Previous issue date: 2012
Resumo: Inspirados em Collet, Galves e Leonardi (2008), a motivação original deste texto é responder a seguinte questão: é possível recuperar a árvore de contextos de uma cadeia de alcance variável através de uma amostra perturbada da cadeia? Inicialmente, consideramos cadeias binárias de ordem infinita nas quais um dos símbolos pode ser modificado com uma probabilidade pequena e fixada. Provamos que as probabilidades de transição da cadeia perturbada estão uniformemente próximas das probabilidades de transição correspondentes da cadeia original se a probabilidade de contaminação é suficientemente pequena. Por meio deste resultado, fomos capazes de responder afirmativamente à pergunta inicial deste trabalho, ou seja, é possível recuperar a árvore de contextos do processo original mesmo utilizando uma amostra contamina no procedimento de estimação. Com isso, mostramos que o estimador da árvore de contextos utilizado é robusto. Em seguida, consideramos o seguinte modelo: dadas duas cadeias de alcance variável, tomando valores num mesmo alfabeto finito, a cada instante do tempo, o novo processo escolhe aleatoriamente um dos dois processos originais com uma probabilidade grande e fixa. A cadeia obtida dessa maneira pode então ser vista como uma perturbação estocástica da cadeia que está sendo escolhida com probabilidade maior. Para esse modelo, obtivemos resultados semelhantes aos obtidos para o modelo inicial
Abstract: Inspired by Collet, Galves and Leonardi (2008), the original motivation of this paper is to answer the following question: Is it possible to recover the context tree of a length variable chain range through a disturbed sample of chain? Initially consider binary chains of infinite order in which one of the symbols can be modified with a small and fixed probability. We prove that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain if the probability of contamination is small enough. Through this result, we were able to answer affirmatively to the initial question of this work, i.e., it is possible to recover the context tree of the original process using a sample contaminates the estimation procedure. With this, we show that the estimator of the context tree used is robust. Next, consider the following model: given two length variable chains, taking values in the same finite alphabet, at each instant of time, the new process randomly chooses one of the two processes with a large and fixed probability. The chain obtained with greater probability can be seen as a stochastic disturbance of the original chain. For this model, we obtained similar results to the those obtained for the initial model
Doutorado
Estatistica
Doutor em Estatística
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Przybylko, Marcin. "Stochastic games and their complexities." Thesis, Nouvelle Calédonie, 2019. http://www.theses.fr/2019NCAL0004.
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Nous étudions les jeux ramifiés introduits par Mio pour définir la sémantique du μ-calcul modal stochastique. Ces jeux stochastiques infinis à information imparfaite joués tour à tour par deux joueurs forment une sous-classe des jeux infinis à somme nulle. Elles étendent les jeux de Gale- Stewart en ce que chaque partie peut se scinder en sous-parties qui se déroulent indépendamment et simultanément. En conséquence, chaque partie a une structure arborescente, contrairement à la structure linéaire des parties des jeux de Gale-Stewart.Dans cette thèse, nous étudions les jeux ramifiés réguliers. Ceux-ci ont pour caractéristique d’avoir leurs ensembles gagnants régulières, c’est à dire, des ensembles d’arbres infinis reconnus par automates finis d’arbres. Nous nous intéressons aux problèmes de détermination, de calcul des valeurs de jeux ramifiés réguliers et de calcul effectif de la mesure d’un ensemble régulier d’arbres. De plus, nous utilisons des données réelles pour présenter comment on peut employer des techniques de la théorie des jeux stochastiques en pratique. Nous proposons une procédure générale qui à partir d’une série temporelle crée un modèle réactif capable de prédire l’évolution du système. Ce modèle facilite aussi les choix des stratégies permettant d’atteindre certains objectifs prédéfinis. La procédure nous sert ensuite à créer un jeux basé sur les processus décisionnels de Markov. Le jeu obtenu peut être utilisé pour prédire et contrôler le niveau d’infestation d’un verger expérimentalWe study a class of games introduced by Mio to capture the probabilistic μ-calculi called branching games. They are a subclass of stochastic two-player zero-sum turn-based infinite-time games of imperfect information. Branching games extend Gale-Stewart games by allowing players to split the execution of a play into new concurrent sub-games that continue their execution independently. In consequence, the play of a branching game has a tree-like structure, as opposed to linearly structured plays of Gale-Stewart games.In this thesis, we focus our attention on regular branching games. Those are the branching games whose pay-off functions are the indicator functions of regular sets of infinite trees, i.e. the sets recognisable by finite tree automata. We study the problems of determinacy, game value computability and the related problem of computing a measure of a regular set of infinite trees.Moreover, we use real-life data to show how to incorporate game-theoretic techniques in practice. We propose a general procedure that given a time series of data extracts a reactive model that can be used to predict the evolution of the system and advise on the strategies to achieve predefined goals. We use the procedure to create a game based on Markov decision processes that is used to predict and control level of pest in a tropical fruit farm
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Denkl, Stephan [Verfasser]. "Second-order approximations to pricing and hedging in presence of jumps and stochastic volatility / Stephan Denkl." Kiel : Universitätsbibliothek Kiel, 2013. http://d-nb.info/1035182157/34.
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Soberanis, Policarpio Antonio. "Risk optimization with p-order conic constraints." Diss., University of Iowa, 2009. https://ir.uiowa.edu/etd/437.
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My dissertation considers solving of linear programming problems with p-order conic constraints that are related to a class of stochastic optimization models with risk objective or constraints that involve higher moments of loss distributions. The general proposed approach is based on construction of polyhedral approximations for p-order cones, thereby approximating the non-linear convex p-order conic programming problems using linear programming models. It is shown that the resulting LP problems possess a special structure that makes them amenable to efficient decomposition techniques. The developed algorithms are tested on the example of portfolio optimization problem with higher moment coherent risk measures that reduces to a p-order conic programming problem. The conducted case studies on real financial data demonstrate that the proposed computational techniques compare favorably against a number of benchmark methods, including second-order conic programming methods.
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Xie, Xuping. "Large Eddy Simulation Reduced Order Models." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/77626.
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This dissertation uses spatial filtering to develop a large eddy simulation reduced order model (LES-ROM) framework for fluid flows. Proper orthogonal decomposition is utilized to extract the dominant spatial structures of the system. Within the general LES-ROM framework, two approaches are proposed to address the celebrated ROM closure problem. No phenomenological arguments (e.g., of eddy viscosity type) are used to develop these new ROM closure models.
The first novel model is the approximate deconvolution ROM (AD-ROM), which uses methods from image processing and inverse problems to solve the ROM closure problem. The AD-ROM is investigated in the numerical simulation of a 3D flow past a circular cylinder at a Reynolds number $Re=1000$. The AD-ROM generates accurate results without any numerical dissipation mechanism. It also decreases the CPU time of the standard ROM by orders of magnitude.
The second new model is the calibrated-filtered ROM (CF-ROM), which is a data-driven ROM. The available full order model results are used offline in an optimization problem to calibrate the ROM subfilter-scale stress tensor. The resulting CF-ROM is tested numerically in the simulation of the 1D Burgers equation with a small diffusion parameter. The numerical results show that the CF-ROM is more efficient than and as accurate as state-of-the-art ROM closure models.Ph. D.
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Khirirat, Sarit. "First-Order Algorithms for Communication Efficient Distributed Learning." Licentiate thesis, KTH, Reglerteknik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-263738.
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Technological developments in devices and storages have made large volumes of data collections more accessible than ever. This transformation leads to optimization problems with massive data in both volume and dimension. In response to this trend, the popularity of optimization on high performance computing architectures has increased unprecedentedly. These scalable optimization solvers can achieve high efficiency by splitting computational loads among multiple machines. However, these methods also incur large communication overhead. To solve optimization problems with millions of parameters, communication between machines has been reported to consume up to 80% of the training time. To alleviate this communication bottleneck, many optimization algorithms with data compression techniques have been studied. In practice, they have been reported to significantly save communication costs while exhibiting almost comparable convergence as the full-precision algorithms. To understand this intuition, we develop theory and techniques in this thesis to design communication-efficient optimization algorithms. In the first part, we analyze the convergence of optimization algorithms with direct compression. First, we outline definitions of compression techniques which cover many compressors of practical interest. Then, we provide the unified analysis framework of optimization algorithms with compressors which can be either deterministic or randomized. In particular, we show how the tuning parameters of compressed optimization algorithms must be chosen to guarantee performance. Our results show explicit dependency on compression accuracy and delay effect due to asynchrony of algorithms. This allows us to characterize the trade-off between iteration and communication complexity under gradient compression. In the second part, we study how error compensation schemes can improve the performance of compressed optimization algorithms. Even though convergence guarantees of optimization algorithms with error compensation have been established, there is very limited theoretical support which guarantees improved solution accuracy. We therefore develop theoretical explanations, which show that error compensation guarantees arbitrarily high solution accuracy from compressed information. In particular, error compensation helps remove accumulated compression errors, thus improving solution accuracy especially for ill-conditioned problems. We also provide strong convergence analysis of error compensation on parallel stochastic gradient descent across multiple machines. In particular, the error-compensated algorithms, unlike direct compression, result in significant reduction in the compression error. Applications of the algorithms in this thesis to real-world problems with benchmark data sets validate our theoretical results.Utvecklandet av kommunikationsteknologi och datalagring har gjort stora mängder av datasamlingar mer tillgängliga än någonsin. Denna förändring leder till numeriska optimeringsproblem med datamängder med stor skala i volym och dimension. Som svar på denna trend har populariteten för högpresterande beräkningsarkitekturer ökat mer än någonsin tidigare. Skalbara optimeringsverktyg kan uppnå hög effektivitet genom att fördela beräkningsbördan mellan ett flertal maskiner. De kommer dock i praktiken med ett pris som utgörs av betydande kommunikationsomkostnader. Detta orsakar ett skifte i flaskhalsen för prestandan från beräkningar till kommunikation. När lösning av verkliga optimeringsproblem sker med ett stort antal parametrar, dominerar kommunikationen mellan maskiner nästan 80% av träningstiden. För att minska kommunikationsbelastningen, har ett flertal kompressionstekniker föreslagits i litteraturen. Även om optimeringsalgoritmer som använder dessa kompressorer rapporteras vara lika konkurrenskraftiga som sina motsvarigheter med full precision, dras de med en förlust av noggrannhet. För att ge en uppfattning om detta, utvecklar vi i denna avhandling teori och tekniker för att designa kommunikations-effektiva optimeringsalgoritmer som endast använder information med låg precision. I den första delen analyserar vi konvergensen hos optimeringsalgoritmer med direkt kompression. Först ger vi en översikt av kompressionstekniker som täcker in många kompressorer av praktiskt intresse. Sedan presenterar vi ett enhetligt analysramverk för optimeringsalgoritmer med kompressorer, som kan vara antingen deterministiska eller randomiserade. I synnerhet visas val av parametrar i komprimerade optimeringsalgoritmer som avgörs av kompressorns parametrar som garanterar konvergens. Våra konvergensgarantier visar beroende av kompressorns noggrannhet och fördröjningseffekter på grund av asynkronicitet hos algoritmer. Detta låter oss karakterisera avvägningen mellan iterations- och kommunikations-komplexitet när kompression används. I den andra delen studerarvi hög prestanda hos felkompenseringsmetoder för komprimerade optimeringsalgoritmer. Även om konvergensgarantier med felkompensering har etablerats finns det väldigt begränsat teoretiskt stöd för konkurrenskraftiga konvergensgarantier med felkompensering. Vi utvecklar därför teoretiska förklaringar, som visar att användande av felkompensering garanterar godtyckligt hög lösningsnoggrannhet från komprimerad information. I synnerhet bidrar felkompensering till att ta bort ackumulerade kompressionsfel och förbättrar därmed lösningsnoggrannheten speciellt för illa konditionerade kvadratiska optimeringsproblem. Vi presenterar också stark konvergensanalys för felkompensering tillämpat på stokastiska gradientmetoder med ett kommunikationsnätverk innehållande ett flertal maskiner. De felkompenserade algoritmerna resulterar, i motsats till direkt kompression, i betydande reducering av kompressionsfelet. Simuleringar av algoritmer i denna avhandling på verkligaproblem med referensdatamängder validerar våra teoretiska resultat.
QC20191120
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Li, Xiaohu. "Security Analysis on Network Systems Based on Some Stochastic Models." ScholarWorks@UNO, 2014. http://scholarworks.uno.edu/td/1931.
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Due to great effort from mathematicians, physicists and computer scientists, network science has attained rapid development during the past decades. However, because of the complexity, most researches in this area are conducted only based upon experiments and simulations, it is critical to do research based on theoretical results so as to gain more insight on how the structure of a network affects the security. This dissertation introduces some stochastic and statistical models on certain networks and uses a k-out-of-n tolerant structure to characterize both logically and physically the behavior of nodes. Based upon these models, we draw several illuminating results in the following two aspects, which are consistent with what computer scientists have observed in either practical situations or experimental studies.
Suppose that the node in a P2P network loses the designed function or service when some of its neighbors are disconnected. By studying the isolation probability and the durable time of a single user, we prove that the network with the user's lifetime having more NWUE-ness is more resilient in the sense of having a smaller probability to be isolated by neighbors and longer time to be online without being interrupted. Meanwhile, some preservation properties are also studied for the durable time of a network. Additionally, in order to apply the model in practice, both graphical and nonparametric statistical methods are developed and are employed to a real data set.
On the other hand, a stochastic model is introduced to investigate the security of network systems based on their vulnerability graph abstractions. A node loses its designed function when certain number of its neighbors are compromised in the sense of being taken over by the malicious codes or the hacker. The attack compromises some nodes, and the victimized nodes become accomplices. We derived an equation to solve the probability for a node to be compromised in a network. Since this equation has no explicit solution, we also established new lower and upper bounds for the probability.
The two models proposed herewith generalize existing models in the literature, the corresponding theoretical results effectively improve those known results and hence carry an insight on designing a more secure system and enhancing the security of an existing system.
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Kelome, Djivèdé Armel. "Viscosity solutions of second order equations in a separable Hilbert space and applications to stochastic optimal control." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/29159.
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Auffredic, Jérémy. "A second order Runge–Kutta method for the Gatheral model." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-49170.
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In this thesis, our research focus on a weak second order stochastic Runge–Kutta method applied to a system of stochastic differential equations known as the Gatheral Model. We approximate numerical solutions to this system and investigate the rate of convergence of our method. Both call and put options are priced using Monte-Carlo simulation to investigate the order of convergence. The numerical results show that our method is consistent with the theoretical order of convergence of the Monte-Carlo simulation. However, in terms of the Runge-Kutta method, we cannot accept the consistency of our method with the theoretical order of convergence without further research.
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Szekely, Tamas. "Stochastic modelling and simulation in cell biology." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:f9b8dbe6-d96d-414c-ac06-909cff639f8c.
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Modelling and simulation are essential to modern research in cell biology. This thesis follows a journey starting from the construction of new stochastic methods for discrete biochemical systems to using them to simulate a population of interacting haematopoietic stem cell lineages. The first part of this thesis is on discrete stochastic methods. We develop two new methods, the stochastic extrapolation framework and the Stochastic Bulirsch-Stoer methods. These are based on the Richardson extrapolation technique, which is widely used in ordinary differential equation solvers. We believed that it would also be useful in the stochastic regime, and this turned out to be true. The stochastic extrapolation framework is a scheme that admits any stochastic method with a fixed stepsize and known global error expansion. It can improve the weak order of the moments of these methods by cancelling the leading terms in the global error. Using numerical simulations, we demonstrate that this is the case up to second order, and postulate that this also follows for higher order. Our simulations show that extrapolation can greatly improve the accuracy of a numerical method. The Stochastic Bulirsch-Stoer method is another highly accurate stochastic solver. Furthermore, using numerical simulations we find that it is able to better retain its high accuracy for larger timesteps than competing methods, meaning it remains accurate even when simulation time is speeded up. This is a useful property for simulating the complex systems that researchers are often interested in today. The second part of the thesis is concerned with modelling a haematopoietic stem cell system, which consists of many interacting niche lineages. We use a vectorised tau-leap method to examine the differences between a deterministic and a stochastic model of the system, and investigate how coupling niche lineages affects the dynamics of the system at the homeostatic state as well as after a perturbation. We find that larger coupling allows the system to find the optimal steady state blood cell levels. In addition, when the perturbation is applied randomly to the entire system, larger coupling also results in smaller post-perturbation cell fluctuations compared to non-coupled cells. In brief, this thesis contains four main sets of contributions: two new high-accuracy discrete stochastic methods that have been numerically tested, an improvement that can be used with any leaping method that introduces vectorisation as well as how to use a common stepsize adapting scheme, and an investigation of the effects of coupling lineages in a heterogeneous population of haematopoietic stem cell niche lineages.
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Lan, Guanghui. "Convex optimization under inexact first-order information." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29732.
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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.Committee Chair: Arkadi Nemirovski; Committee Co-Chair: Alexander Shapiro; Committee Co-Chair: Renato D. C. Monteiro; Committee Member: Anatoli Jouditski; Committee Member: Shabbir Ahmed. Part of the SMARTech Electronic Thesis and Dissertation Collection.