Dissertations / Theses on the topic 'Stochastic'
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Abi, Jaber Eduardo. "Stochastic Invariance and Stochastic Volterra Equations." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLED025/document.
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La présente thèse traite de la théorie des équations stochastiques en dimension finie. Dans la première partie, nous dérivons des conditions géométriques nécessaires et suffisantes sur les coefficients d’une équation différentielle stochastique pour l’existence d’une solution contrainte à rester dans un domaine fermé, sous de faibles conditions de régularité sur les coefficients.Dans la seconde partie, nous abordons des problèmes d’existence et d’unicité d’équations de Volterra stochastiques de type convolutif. Ces équations sont en général non-Markoviennes. Nous établissons leur correspondance avec des équations en dimension infinie ce qui nous permet de les approximer par des équations différentielles stochastiques Markoviennes en dimension finie.Enfin, nous illustrons nos résultats par une application en finance mathématique, à savoir la modélisation de la volatilité rugueuse. En particulier, nous proposons un modèle à volatilité stochastique assurant un bon compromis entre flexibilité et tractabilitéThe present thesis deals with the theory of finite dimensional stochastic equations.In the first part, we derive necessary and sufficient geometric conditions on the coefficients of a stochastic differential equation for the existence of a constrained solution, under weak regularity on the coefficients. In the second part, we tackle existence and uniqueness problems of stochastic Volterra equations of convolution type. These equations are in general non-Markovian. We establish their correspondence with infinite dimensional equations which allows us to approximate them by finite dimensional stochastic differential equations of Markovian type. Finally, we illustrate our findings with an application to mathematical finance, namely rough volatility modeling. We design a stochastic volatility model with an appealing trade-off between flexibility and tractability
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Yang, Weiye. "Stochastic analysis and stochastic PDEs on fractals." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:43a7af74-c531-424a-9f3d-4277138affbb.
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Stochastic analysis on fractals is, as one might expect, a subfield of analysis on fractals. An intuitive starting point is to observe that on many fractals, one can define diffusion processes whose law is in some sense invariant with respect to the symmetries and self-similarities of the fractal. These can be interpreted as fractal-valued counterparts of standard Brownian motion on Rd. One can study these diffusions directly, for example by computing heat kernel and hitting time estimates. On the other hand, by associating the infinitesimal generator of the fractal-valued diffusion with the Laplacian on Rd, it is possible to pose stochastic partial differential equations on the fractal such as the stochastic heat equation and stochastic wave equation. In this thesis we investigate a variety of questions concerning the properties of diffusions on fractals and the parabolic and hyperbolic SPDEs associated with them. Key results include an extension of Kolmogorov's continuity theorem to stochastic processes indexed by fractals, and existence and uniqueness of solutions to parabolic SPDEs on fractals with Lipschitz data.
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Fei, Lin. "On a stochastic optimization technique : stochastic probing /." The Ohio State University, 1992. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487777901661535.
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Ozkan, Pelin. "Analysis Of Stochastic And Non-stochastic Volatility Models." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/3/12605421/index.pdf.
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Changing in variance or volatility with time can be modeled as deterministic by using autoregressive conditional heteroscedastic (ARCH) type models, or as stochastic by using stochastic volatility (SV) models. This study compares these two kinds of models which are estimated on Turkish / USA exchange rate data. First, a GARCH(1,1) model is fitted to the data by using the package E-views and then a Bayesian estimation procedure is used for estimating an appropriate SV model with the help of Ox code. In order to compare these models, the LR test statistic calculated for non-nested hypotheses is obtained.
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Yakowitz, Diana Schadl. "Two-stage stochastic linear programming: Stochastic decomposition approaches." Diss., The University of Arizona, 1991. http://hdl.handle.net/10150/185342.
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Stochastic linear programming problems are linear programming problems for which one or more data elements are described by random variables. Two-stage stochastic linear programming problems are problems in which a first stage decision is made before the random variables are observed. A second stage, or recourse decision, which varies with these observations compensates for any deficiencies which result from the earlier decision. Many applications areas including water resources, industrial management, economics and finance lead to two-stage stochastic linear programs with recourse. In this dissertation, two algorithms for solving stochastic linear programming problems with recourse are developed and tested. The first is referred to as Quadratic Stochastic Decomposition (QSD). This algorithm is an enhanced version of the Stochastic Decomposition (SD) algorithm of Higle and Sen (1988). The enhancements were designed to increase the computational efficiency of the SD algorithm by introducing a quadratic proximal term in the master program objective function and altering the manner in which the recourse function approximations are updated. We show that every accumulation point of an easily identifiable subsequence of points generated by the algorithm are optimal solutions to the stochastic program with probability 1. The various combinations of the enhancements are empirically investigated in a computational experiment using operations research problems from the literature. The second algorithm is an SD based algorithm for solving a stochastic linear program in which the recourse problem appears in the constraint set. This algorithm involves the use of an exact penalty function in the master program. We find that under certain conditions every accumulation point of a sequence of points generated by the algorithm is an optimal solution to the recourse constrained stochastic program, with probability 1. This algorithm is tested on several operations research problems.
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Kůdela, Jakub. "Advanced Decomposition Methods in Stochastic Convex Optimization." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-403864.
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Při práci s úlohami stochastického programování se často setkáváme s optimalizačními problémy, které jsou příliš rozsáhlé na to, aby byly zpracovány pomocí rutinních metod matematického programování. Nicméně, v některých případech mají tyto problémy vhodnou strukturu, umožňující použití specializovaných dekompozičních metod, které lze použít při řešení rozsáhlých optimalizačních problémů. Tato práce se zabývá dvěma třídami úloh stochastického programování, které mají speciální strukturu, a to dvoustupňovými stochastickými úlohami a úlohami s pravděpodobnostním omezením, a pokročilými dekompozičními metodami, které lze použít k řešení problému v těchto dvou třídách. V práci popisujeme novou metodu pro tvorbu “warm-start” řezů pro metodu zvanou “Generalized Benders Decomposition”, která se používá při řešení dvoustupňových stochastických problémů. Pro třídu úloh s pravděpodobnostním omezením zde uvádíme originální dekompoziční metodu, kterou jsme nazvali “Pool & Discard algoritmus”. Užitečnost popsaných dekompozičních metod je ukázána na několika příkladech a inženýrských aplikacích.
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Andersson, Kristina. "Stochastic Volatility." Thesis, Uppsala University, Department of Mathematics, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121722.
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Huang, Chueng-Chiu S. "Stochastic scheduling." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/24834.
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Dean, David Stanley. "Stochastic dynamics." Thesis, University of Cambridge, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318048.
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Vedin, Robert. "Stochastic Resonance." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-193632.
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Noise is often viewed as something unfortunate and unavoidable, however with the development of Stochastic Resonance (SR) theory it has been shown to have beneficial effects in many non-linear systems. We have explored the SR phenomenon via numerical simulations of two such systems. The first one is a one-dimensional Brownian particle in a bi-stable potential and the second a simple model of a signal neuron both subject to a periodic input signal. We have investigated the system responses for different input signal frequencies and noise levels in order to determine both an optimal noise level and any dependencies upon the input signal frequency.
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Chugreeva, Olga [Verfasser], Christof Erich [Akademischer Betreuer] Melcher, and Maria Gabrielle [Akademischer Betreuer] Westdickenberg. "Stochastics meets applied analysis : stochastic Ginzburg-Landau vortices and stochastic Landau-Lifshitz-Gilbert equation / Olga Chugreeva ; Christof Erich Melcher, Maria Gabrielle Westdickenberg." Aachen : Universitätsbibliothek der RWTH Aachen, 2016. http://d-nb.info/1156922305/34.
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Jayawardena, Thusitha Senadirage. "Self-optimizing stochastic systems: Applications to stochastic shortest path problem, stochastic traveling salesman problem, and queueing systems." Diss., The University of Arizona, 1990. http://hdl.handle.net/10150/185025.
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We investigate stochastic systems which have a set of control parameters and a performance criterion. By operating the system at fixed control parameters, noisy performance values are observed. (The values are noisy due to the inherent stochastic nature of the system.) Certain relevant distributions of the system are assumed unavailable. The task is to develop algorithms that guide the system to optimal parameter settings based on its operating history. Consider the stochastic shortest path problem, where the time to traverse an edge is given by a random variable whose distribution is unavailable explicitly. The optimality criterion (to be maximized) is the probability of going from a given source node to a given terminal node within a specified critical time period. By choosing a particular path and traversing it, realizations of the distributions, i.e. time to go from the source node to the terminal node on that path are observed. Or consider the M/M/1 queue. Here, the control parameter is the average service time. The performance criterion is the sum of cost of the server and cost of system time of a customer in steady-state. By choosing a particular average service time and serving accordingly, a noisy observation of the total cost is obtained. We combine an asymptotically optimal random search method for finding the global optimum of a function with problem-specific local search techniques. Such a combination results in efficient solution procedures for the above problems. This conclusion is reached by applying the procedure to problems for which the optimum solutions are known. The main contribution of the study is in demonstrating that "reasonable" performance can be achieved for the proposed optimization problems in "reasonable" time by exploiting problem-specific structures to advantage. The generality of the method should allow others to use it in different optimization settings than ours. Also, the self-optimizing aspect of these methods and the stochastic versions of the local search techniques are new.
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Archer, Sandra. "STOCHASTIC RESOURCE CONSTRAINED PROJECT SCHEDULING WITH STOCHASTIC TASK INSERTION PROBLEMS." Doctoral diss., University of Central Florida, 2008. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3520.
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The area of focus for this research is the Stochastic Resource Constrained Project Scheduling Problem (SRCPSP) with Stochastic Task Insertion (STI). The STI problem is a specific form of the SRCPSP, which may be considered to be a cross between two types of problems in the general form: the Stochastic Project Scheduling Problem, and the Resource Constrained Project Scheduling Problem. The stochastic nature of this problem is in the occurrence/non-occurrence of tasks with deterministic duration. Researchers Selim (2002) and Grey (2007) laid the groundwork for the research on this problem. Selim (2002) developed a set of robustness metrics and used these to evaluate two initial baseline (predictive) scheduling techniques, optimistic (0% buffer) and pessimistic (100% buffer), where none or all of the stochastic tasks were scheduled, respectively. Grey (2007) expanded the research by developing a new partial buffering strategy for the initial baseline predictive schedule for this problem and found the partial buffering strategy to be superior to Selim s extreme buffering approach. The current research continues this work by focusing on resource aspects of the problem, new buffering approaches, and a new rescheduling method. If resource usage is important to project managers, then a set of metrics that describes changes to the resource flow would be important to measure between the initial baseline predictive schedule and the final as-run schedule. Two new sets of resource metrics were constructed regarding resource utilization and resource flow. Using these new metrics, as well as the Selim/Grey metrics, a new buffering approach was developed that used resource information to size the buffers. The resource-sized buffers did not show to have significant improvement over Grey s 50% buffer used as a benchmark. The new resource metrics were used to validate that the 50% buffering strategy is superior to the 0% or 100% buffering by Selim. Recognizing that partial buffers appear to be the most promising initial baseline development approach for STI problems, and understanding that experienced project managers may be able to predict stochastic probabilities based on prior projects, the next phase of the research developed a new set of buffering strategies where buffers are inserted that are proportional to the probability of occurrence. The results of this proportional buffering strategy were very positive, with the majority of the metrics (both robustness and resource), except for stability metrics, improved by using the proportional buffer. Finally, it was recognized that all research thus far for the SRCPSP with STI focused solely on the development of predictive schedules. Therefore, the final phase of this research developed a new reactive strategy that tested three different rescheduling points during schedule eventuation when a complete rescheduling of the latter portion of the schedule would occur. The results of this new reactive technique indicate that rescheduling improves the schedule performance in only a few metrics under very specific network characteristics (those networks with the least restrictive parameters). This research was conducted with extensive use of Base SAS v9.2 combined with SAS/OR procedures to solve project networks, solve resource flow problems, and implement reactive scheduling heuristics. Additionally, Base SAS code was paired with Visual Basic for Applications in Excel 2003 to implement an automated Gantt chart generator that provided visual inspection for validation of the repair heuristics. The results of this research when combined with the results of Selim and Grey provide strong guidance for project managers regarding how to develop baseline predictive schedules and how to reschedule the project as stochastic tasks (e.g. unplanned work) do or do not occur. Specifically, the results and recommendations are provided in a summary tabular format that describes the recommended initial baseline development approach if a project manager has a good idea of the level and location of the stochasticity for the network, highlights two cases where rescheduling during schedule eventuation may be beneficial, and shows when buffering proportional to the probability of occurrence is recommended, or not recommended, or the cases where the evidence is inconclusive.Ph.D.
Department of Industrial Engineering and Management Systems
Engineering and Computer Science
Industrial Engineering PhD
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Archer, Sandra. "Stochastic resource constrained project scheduling with stochastic task insertions problems." Orlando, Fla. : University of Central Florida, 2008. http://purl.fcla.edu/fcla/etd/CFE0002491.
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Li, Haijun. "Contributions to the theory of stochastic convexity and stochastic majorization." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186817.
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This dissertation presents some contributions to the theory of stochastic convexity and stochastic majorization. In the first part of this dissertation, we develop an operator-analytic approach to study temporal stochastic convexity and concavity of Markov processes. We obtain sufficient and necessary conditions for the process {X(t),t ∊ S} which imply that the expectation Ef(X(t)) is a monotone convex (concave) function of t whenever f is a monotone convex (concave) function. Our operator-analytic approach is quite powerful, but not as intuitive as sample path approaches used in other works. However, using it, we can obtain results that we could not obtain otherwise. In particular, we show that a result of Shaked and Shanthikumar is incorrect and we prove two alternative versions of it. In the second part of this dissertation, we discuss some applications of stochastic convexity. Using the F-monotonicity and F-convexity developed in the first part of this dissertation, we obtain relations among the several notions of stochastic convexity and stochastic majorization, and characterize the relationship between stochastic submodularity and stochastic rearrangement. These results generalize and extend several known results in the literature. Applications of our results to stochastic allocation problems are also discussed.
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Fox, Michael Jacob. "Stochastic self-assembly." Thesis, Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/34741.
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We present methods for distributed self-assembly that utilize simple rule-of-thumb control and communication schemes providing probabilistic performance guarantees. These methods represents a staunch departure from existing approaches that require more sophisticated control and communication, but provide deterministic guarantees. In particular, we show that even under severe communication restrictions, any assembly described by an acyclic weighted graph can be assembled with a rule set that is linear in the number of nodes contained in the desired assembly graph. We introduce the concept of stochastic
stability to the self-assembly problem and show that stochastic stability of desirable configurations can be exploited to provide probabilistic performance guarantees for the process. Relaxation of the communication restrictions allows simple approaches giving deterministic guarantees. We establish a clear relationship between availability of communication and convergence properties. We consider Self-assembly tasks for the cases of many and few
agents as well as large and small assembly goals. We analyze sensitivity of the presented process to communication errors as well as ill-intentioned agents. We discuss convergence rates of the presented process and directions for improving them.
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Ozkan, Erhun. "Stochastic Inventory Modelling." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/3/12612097/index.pdf.
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In this master thesis study, new inventory control mechanisms are developed for the
repairables in Nedtrain. There is a multi-item, multi echelon system with a continuous
review and one for one replenishment policy and there are different demand supply
options in each control mechanism. There is an aggregate mean waiting time constraint
in each local warehouse and the objective is to minimize the total system cost. The base
stock levels in each warehouse are determined with an approximation method. Then
different demand supply options are compared with each other.
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Prähofer, Michael. "Stochastic Surface Growth." Diss., lmu, 2003. http://nbn-resolving.de/urn:nbn:de:bvb:19-13818.
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Saygun, Yakup. "Computational Stochastic Morphogenesis." Thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-257096.
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Self-organizing patterns arise in a variety of ways in nature, the complex patterning observed on animal coats is such an example. It is already known that the mechanisms responsible for pattern formation starts at the developmental stage of an embryo. However, the actual process determining cell fate has been, and still is, unknown. The mathematical interest for pattern formation emerged from the theories formulated by the mathematician and computer scientist Alan Turing in 1952. He attempted to explain the mechanisms behind morphogenesis and how the process of spatial cell differentiation from homogeneous cells lead to organisms with different complexities and shapes. Turing formulated a mathematical theory and proposed a reaction-diffusion system where morphogens, a postulated chemically active substance, moderated the whole mechanism. He concluded that this process was stable as long as diffusion was neglected; otherwise this would lead to a diffusion-driven instability, which is the fundamental part of pattern formation. The mathematical theory describing this process consists of solving partial differential equations and Turing considered deterministic reaction-diffusion systems. This thesis will start with introducing the reader to the problem and then gradually build up the mathematical theory needed to get an understanding of the stochastic reaction-diffusion systems that is the focus of the thesis. This study will to a large extent simulate stochastic systems using numerical computations and in order to be computationally feasible a compartment-based model will be used. Noise is an inherent part of such systems, so the study will also discuss the effects of noise and morphogen kinetics on different geometries with boundaries of different complexities from one-dimensional cases up to three-dimensions.
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Le, Truc. "Stochastic volatility models." Monash University, School of Mathematical Sciences, 2005. http://arrow.monash.edu.au/hdl/1959.1/5181.
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Sanyal, Suman. "Stochastic dynamic equations." Diss., Rolla, Mo. : Missouri University of Science and Technology, 2008. http://scholarsmine.mst.edu/thesis/pdf/Sanyal_09007dcc80519030.pdf.
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Thesis (Ph. D.)--Missouri University of Science and Technology, 2008.Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed August 21, 2008) Includes bibliographical references (p. 124-131).
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Bocharov, Boris. "Stochastic evolution inclusions." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/3772.
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This work is concerned with an evolution inclusion of a form, in a triple of spaces \V -> H -> V*", where U is a continuous non-decreasing process, M is a locally square-integrable martingale and the operators A (multi-valued) and B satisfy some monotonicity condition, a coercivity condition and a condition on growth in u. An existence and uniqueness theorem is proved for the solutions, using semi-implicit time-discretization schemes. Examples include evolution equations and inclusions driven by square integrable Levy martingales.
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Graham, B. T. "Interacting stochastic systems." Thesis, University of Cambridge, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.599589.
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The Ising model was suggested by Lenz in 1920. It is a probabilistic model for ferromagnetism. Magnetization can then be explored as correlation between spin random variables on a graph. Bond percolation was introduced by Simon Broadbent and John Hammersley in 1957. It is a model for long range order. Edges of a lattice graph are declared open, independently, with some probability p, and clusters of open edges are studied. Both these models can be understood as aspects of the random-cluster model. In this thesis we study various aspects of mathematical statistical mechanics. In Chapter 2 we create a diluted version of the random-cluster model. This allows the coupling of the Ising model to the random-cluster model to be extended to include the Blume-Capel model. Crucially, it retains some of the key properties of its parent model. This enables much of the random-cluster technology to be carried forward. The key issue for bond percolation concerns the fraction of open edges required in order to have long range connectivity. Harry Kesten proved that this fraction is precisely one half for the square planar lattice. Recent development in the theory of influence and sharp thresholds allowed Béla Bollobás and Oliver Riordan to simplify parts of his proof. In Chapter 3 we extend an influence result to apply to monotonic measures. This allows sharp thresholds to be shown for certain families of stochastically increasing monotonic distributions, including random-cluster measures. In Chapter 4 we study time to convergence for a mean-field zero-range process. The problem was motivated by the canonical ensemble model of energy levels used in the derivation of Maxwell-Boltzmann distributions. By considering the entropy of the system, we show that the empirical distribution rapidly converges – in the sense of Kullback-Leibler divergence – to a geometric distribution. The proof utilizes arguments of spectral gap and log Sobolev type.
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Rikoski, Richard J. (Richard James) 1976. "Delayed stochastic mapping." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/91338.
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Magureanu, Stefan. "Structured Stochastic Bandits." Licentiate thesis, KTH, Reglerteknik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-182816.
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In this thesis we address the multi-armed bandit (MAB) problem with stochastic rewards and correlated arms. Particularly, we investigate the case when the expected rewards are a Lipschitz function of the arm, and the learning to rank problem, as viewed from a MAB perspective. For the former, we derive a problem specific lower bound and propose both an asymptotically optimal algorithm (OSLB) and a (pareto)optimal, algorithm (POSLB). For the latter, we construct the regret lower bound and determine its closed form for some particular settings, as well as propose two asymptotically optimal algorithms PIE and PIE-C. For all algorithms mentioned above, we present performance analysis in the form of theoretical regret guarantees as well as numerical evaluation on artificial datasets as well as real-world datasets, in the case of PIE and PIE-C.QC 20160223
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Chen, Xiaoli. "Stochastic differential inclusions." Thesis, University of Edinburgh, 2006. http://hdl.handle.net/1842/13367.
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Stochastic differential inclusions (SDIs) on Rd have been investigated in this thesis, dx(t) Î a(t, x(t))dt + (t, x (t)d where a is a maximal monotone mapping, b is a Lipschitz continuous function, and w is a Wiener process. The principal aim of this work is to present some new results on solvability and approximations of SDIs. Two methods are adapted to obtain our results: the method of minimization and the method of implicit approximation. We interpret the method of monotonicity as a method of constructing minimizers to certain convex functions. Under the monotonicity condition and the usual linear growth condition, the solutions are characterized as the minimizers of convex functionals, and are constructed via implicit approximations. Implicit numerical scheme is given and the result on the rate of convergence is also presented. The ideas of our work are inspired by N.V. Krylov, where stochastic differential equations (SDEs0 in Rd are solved by minimizing convex functions via Euler approximations. Furthermore, since the linear growth condition is too strong, an approach is proposed for truncating maximal monotone functions to get bounded maximal monotone functions. It is a technical challenge in this thesis. Thus the existence of solutions to SDIs is proved under essentially weaker growth condition than the linear growth. For a special case of SDEs, a few of recent results from [5] are generalized. Some existing results of the convergence by implicit numerical schemes are proved under the locally Lipschitz condition. We will show that under certain weaker conditions, if the drift coefficient satisfies one-sided Lipschitz and the diffusion coefficient is Lipschitz continuous, implicit approximations applied to SDEs, converge almost surely to the solution of SDEs. The rate of convergence we get is ¼.
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Mehmeti, Ardit. "Stochastic Inventory Management." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-101526.
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This bachelor thesis is about a stochastic inventory theory and how changes in different parameters affect the cost system. The inventory is based on a stochastic version of an economic quantity order (EOQ) model with planned shortages. For the deterministic EOQ-model with planned shortages there is a convenient formula for optimal order quantity $Q$ minimizing the cost per time unit. For the stochastic version an ($R$,$Q$)-policy is applied where $R$ is a reorder point such that if the inventory level is below $R$ and order is sent and the ordered products arrive after a lead time $L$. Since a formula for the stochastic inventory is not known, optimal choice of $Q$ is numerically obtained by simulations and compared with the optimal $Q$ for the deterministic EOQ with planned shortages. The demand is for simplicity described by a Poisson process. Since having a stochastic inventory model the basic mathematical EOQ formula is inadequate and is replaced with an approximate EOQ formula with planned shortages. By the simulations the accuracy of the EOQ model with planned shortages approximation is investigated and optimal values for some of the parameters are obtained.
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Cooke, Alexander. "Algorithmic Stochastic Music." Case Western Reserve University School of Graduate Studies / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=case1492096098674462.
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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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Zgierski, Jack R. (Jack Robert) Carleton University Dissertation Computer Science. "On stochastic sorting." Ottawa, 1993.
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Gamst, Anthony Collins. "Stochastic burgers flows /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1998. http://wwwlib.umi.com/cr/ucsd/fullcit?p9906479.
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Kammeyer, Thomas E. "Evolving stochastic grammars /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1998. http://wwwlib.umi.com/cr/ucsd/fullcit?p9907601.
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Smith, Aaron D. "Stochastic permanent breaks /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1999. http://wwwlib.umi.com/cr/ucsd/fullcit?p9938588.
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Deng, Hua. "Stochastic nonlinear stabilization /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2001. http://wwwlib.umi.com/cr/ucsd/fullcit?p3007140.
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Li, Le. "Online stochastic algorithms." Thesis, Angers, 2018. http://www.theses.fr/2018ANGE0031.
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Cette thèse travaille principalement sur trois sujets. Le premier concentre sur le clustering en ligne dans lequel nous présentons un nouvel algorithme stochastique adaptatif pour regrouper des ensembles de données en ligne. Cet algorithme repose sur l'approche quasi-bayésienne, avec une estimation dynamique (i.e., dépendant du temps) du nombre de clusters. Nous prouvons que cet algorithme atteint une borne de regret de l'ordre et que cette borne est asymptotiquement minimax sous la contrainte sur le nombre de clusters. Nous proposons aussi une implémentation par RJMCMC. Le deuxième sujet est lié à l'apprentissage séquentiel des courbes principales qui cherche à résumer une séquence des données par une courbe continue. Pour ce faire, nous présentons une procédure basée sur une approche maximum a posteriori pour le quasi-posteriori de Gibbs. Nous montrons que la borne de regret de cet algorithme et celui de sa version adaptative est sous-linéaire en l'horizon temporel T. En outre, nous proposons une implémentation par un algorithme glouton local qui intègre des éléments de sleeping experts et de bandit à plusieurs bras. Le troisième concerne les travaux qui visent à accomplir des tâches pratiques au sein d'iAdvize, l'entreprise qui soutient cette thèse. Il inclut l'analyse des sentiments pour les messages textuels et l'implémentation de chatbot dans lesquels la première est réalisé par les méthodes classiques dans la fouille de textes et les statistiques et la seconde repose sur le traitement du langage naturel et les réseaux de neurones artificielsThis thesis works mainly on three subjects. The first one is online clustering in which we introduce a new and adaptive stochastic algorithm to cluster online dataset. It relies on a quasi-Bayesian approach, with a dynamic (i.e., time-dependent) estimation of the (unknown and changing) number of clusters. We prove that this algorithm has a regret bound of the order of and is asymptotically minimax under the constraint on the number of clusters. A RJMCMC-flavored implementation is also proposed. The second subject is related to the sequential learning of principal curves which seeks to represent a sequence of data by a continuous polygonal curve. To this aim, we introduce a procedure based on the MAP of Gibbs-posterior that can give polygonal lines whose number of segments can be chosen automatically. We also show that our procedure is supported by regret bounds with sublinear remainder terms. In addition, a greedy local search implementation that incorporates both sleeping experts and multi-armed bandit ingredients is presented. The third one concerns about the work which aims to fulfilling practical tasks within iAdvize, the company which supports this thesis. It includes sentiment analysis for textual messages by using methods in both text mining and statistics, and implementation of chatbot based on nature language processing and neural networks
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Vacek, Vladislav. "Stochastické metody v řízení portfolia." Master's thesis, Vysoká škola ekonomická v Praze, 2010. http://www.nusl.cz/ntk/nusl-73894.
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From the beginning of 20th century many studies proved randomness in price evolution of investment instruments. Therefore models respecting this randomness must be used in portfolio management. This thesis' aim is to provide basic theory regarding some of the stochastic methods and show their practical use in real situations.
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Zeytun, Serkan. "Stochastic Volatility, A New Approach For Vasicek Model With Stochastic Volatility." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/3/12606561/index.pdf.
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In the original Vasicek model interest rates are calculated
assuming that volatility remains constant over the period of
analysis. In this study, we constructed a stochastic volatility
model for interest rates. In our model we assumed not only that interest rate process but also the volatility process for interest rates follows the mean-reverting Vasicek model. We derived the density function for the stochastic element of the interest rate process and reduced this density function to a series form. The parameters of our model were estimated by using the method of moments. Finally, we tested the performance of our model using the data of interest rates in Turkey.
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Yuksel, Ayhan. "Credit Risk Modeling With Stochastic Volatility, Jumps And Stochastic Interest Rates." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/2/12609206/index.pdf.
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This thesis presents the modeling of credit risk by using structural approach. Three fundamental questions of credit risk literature are analyzed throughout the research: modeling single firm credit risk, modeling portfolio credit risk and credit risk pricing. First we analyze these questions under the assumptions that firm value follows a geometric Brownian motion and the interest rates are constant. We discuss the weaknesses of the geometric brownian motion assumption in explaining empirical properties of real data. Then we propose a new extended model in which asset value, volatility and interest rates follow affine jump diffusion processes. In our extended model volatility is stochastic, asset value and volatility has correlated jumps and interest rates are stochastic and have jumps. Finally, we analyze the modeling of single firm credit risk and credit risk pricing by using our extended model and show how our model can be used as a solution for the problems we encounter with simple models.
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Pätz, Torben [Verfasser]. "Segmentation of Stochastic Images using Stochastic Partial Differential Equations / Torben Pätz." Bremen : IRC-Library, Information Resource Center der Jacobs University Bremen, 2012. http://d-nb.info/1035219735/34.
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Novotný, Jan. "Modely stochastického programování a jejich aplikace." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2008. http://www.nusl.cz/ntk/nusl-228131.
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Diplomová práce se zabývá stochastickým programováním a jeho aplikací na problém mísení kameniva z oblasti stavebního inženýrství. Teoretická část práce je věnována odvození základních přístupů stochastického programování, tj. optimalizace se zohledněním náhodných vlivů v modelech. V aplikované části je prezentována tvorba vhodných optimalizačních modelů pro mísení kameniva, jejich implementace a výsledky. Práce zahrnuje původní aplikační výsledky docílené při řešení projektu GA ČR reg. čís. 103/08/1658 Pokročilá optimalizace návrhu složených betonových konstrukcí a teoretické výsledky projektu MŠMT České republiky čís. 1M06047 Centrum pro jakost a spolehlivost výroby.
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Ades, Michel. "Topics in stochastic systems, cumulative renewal processes, stochastic control and gradient estimation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq44336.pdf.
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Uhl, Matthias [Verfasser], and Udo [Akademischer Betreuer] Seifert. "Stochastic thermodynamics : from hydrodynamics to stochastic inference / Matthias Uhl ; Betreuer: Udo Seifert." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2021. http://d-nb.info/1233681400/34.
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Hashemi, Fatemeh Sadat. "Sampling Controlled Stochastic Recursions: Applications to Simulation Optimization and Stochastic Root Finding." Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/76740.
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We consider unconstrained Simulation Optimization (SO) problems, that is, optimization problems where the underlying objective function is unknown but can be estimated at any chosen point by repeatedly executing a Monte Carlo (stochastic) simulation. SO, introduced more than six decades ago through the seminal work of Robbins and Monro (and later by Kiefer and Wolfowitz), has recently generated much attention. Such interest is primarily because of SOs flexibility, allowing the implicit specification of functions within the optimization problem, thereby providing the ability to embed virtually any level of complexity. The result of such versatility has been evident in SOs ready adoption in fields as varied as finance, logistics, healthcare, and telecommunication systems.
While SO has become popular over the years, Robbins and Monros original stochastic approximation algorithm and its numerous modern incarnations have seen only mixed success in solving SO problems. The primary reason for this is stochastic approximations explicit reliance on a sequence of algorithmic parameters to guarantee convergence. The theory for choosing such parameters is now well-established, but most such theory focuses on asymptotic performance. Automatically choosing parameters to ensure good finite-time performance has remained vexingly elusive, as evidenced by continuing efforts six decades after the introduction of stochastic approximation! The other popular paradigm to solve SO is what has been called sample-average approximation. Sample-average approximation, more a philosophy than an algorithm to solve SO, attempts to leverage advances in modern nonlinear programming by first constructing a deterministic approximation of the SO problem using a fixed sample size, and then applying an appropriate nonlinear programming method. Sample-average approximation is reasonable as a solution paradigm but again suffers from finite-time inefficiency because of the simplistic manner in which sample sizes are prescribed. It turns out that in many SO contexts, the effort expended to execute the Monte Carlo oracle is the single most computationally expensive operation. Sample-average approximation essentially ignores this issue since, irrespective of where in the search space an incumbent solution resides, prescriptions for sample sizes within sample-average approximation remain the same. Like stochastic approximation, notwithstanding beautiful asymptotic theory, sample-average approximation suffers from the lack of automatic implementations that guarantee good finite-time performance.
In this dissertation, we ask: can advances in algorithmic nonlinear programming theory be combined with intelligent sampling to create solution paradigms for SO that perform well in finite-time while exhibiting asymptotically optimal convergence rates? We propose and study a general solution paradigm called Sampling Controlled Stochastic Recursion (SCSR). Two simple ideas are central to SCSR: (i) use any recursion, particularly one that you would use (e.g., Newton and quasi- Newton, fixed-point, trust-region, and derivative-free recursions) if the functions involved in the problem were known through a deterministic oracle; and (ii) estimate objects appearing within the recursions (e.g., function derivatives) using Monte Carlo sampling to the extent required. The idea in (i) exploits advances in algorithmic nonlinear programming. The idea in (ii), with the objective of ensuring good finite-time performance and optimal asymptotic rates, minimizes Monte Carlo sampling by attempting to balance the estimated proximity of an incumbent solution with the sampling error stemming from Monte Carlo. This dissertation studies the theoretical and practical underpinnings of SCSR, leading to implementable algorithms to solve SO. We first analyze SCSR in a general context, identifying various sufficient conditions that ensure convergence of SCSRs iterates to a solution. We then analyze the nature of such convergence. For instance, we demonstrate that in SCSRs which guarantee optimal convergence rates, the speed of the underlying (deterministic) recursion and the extent of Monte Carlo sampling are intimately linked, with faster recursions permitting a wider range of Monte Carlo effort. With the objective of translating such asymptotic results into usable algorithms, we formulate a family of SCSRs called Adaptive SCSR (A-SCSR) that adaptively determines how much to sample as a recursion evolves through the search space. A-SCSRs are dynamic algorithms that identify sample sizes to balance estimated squared bias and variance of an incumbent solution. This makes the sample size (at every iteration of A-SCSR) a stopping time, thereby substantially complicating the analysis of the behavior of A-SCSRs iterates. That A-SCSR works well in practice is not surprising" the use of an appropriate recursion and the careful sample size choice ensures this. Remarkably, however, we show that A-SCSRs are convergent to a solution and exhibit asymptotically optimal convergence rates under conditions that are no less general than what has been established for stochastic approximation algorithms.
We end with the application of a certain A-SCSR to a parameter estimation problem arising in the context of brain-computer interfaces (BCI). Specifically, we formulate and reduce the problem of probabilistically deciphering the electroencephalograph (EEG) signals recorded from the brain of a paralyzed patient attempting to perform one of a specified set of tasks. Monte Carlo simulation in this context takes a more general view, as the act of drawing an observation from a large dataset accumulated from the recorded EEG signals. We apply A-SCSR to nine such datasets, showing that in most cases A-SCSR achieves correct prediction rates that are between 5 and 15 percent better than competing algorithms. More importantly, due to the incorporated adaptive sampling strategies, A-SCSR tends to exhibit dramatically better efficiency rates for comparable prediction accuracies.Ph. D.
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Karam, Christina Maria. "Stochastic Bilateral Filter and Stochastic Non-local Means for High-dimensional Images." University of Dayton / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=dayton1429728892.
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Bachouch, Achref. "Numerical Computations for Backward Doubly Stochastic Differential Equations and Nonlinear Stochastic PDEs." Thesis, Le Mans, 2014. http://www.theses.fr/2014LEMA1034/document.
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L’objectif de cette thèse est l’étude d’un schéma numérique pour l’approximation des solutions d’équations différentielles doublement stochastiques rétrogrades (EDDSR). Durant les deux dernières décennies, plusieurs méthodes ont été proposées afin de permettre la résolution numérique des équations différentielles stochastiques rétrogrades standards. Dans cette thèse, on propose une extension de l’une de ces méthodes au cas doublement stochastique. Notre méthode numérique nous permet d’attaquer une large gamme d’équations aux dérivées partielles stochastiques (EDPS) nonlinéaires. Ceci est possible par le biais de leur représentation probabiliste en termes d’EDDSRs. Dans la dernière partie, nous étudions une nouvelle méthode des particules dans le cadre des études de protection en neutroniquesThe purpose of this thesis is to study a numerical method for backward doubly stochastic differential equations (BDSDEs in short). In the last two decades, several methods were proposed to approximate solutions of standard backward stochastic differential equations. In this thesis, we propose an extension of one of these methods to the doubly stochastic framework. Our numerical method allows us to tackle a large class of nonlinear stochastic partial differential equations (SPDEs in short), thanks to their probabilistic interpretation. In the last part, we study a new particle method in the context of shielding studies
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Lowe, Wing Wah. "An exploration of stochastic decomposition algorithms for stochastic linear programs with recourse." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186667.
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Stochastic linear programs are linear programs in which some of the problem data are random variables. The particular kind of programs that we study belong to the recourse model. Under this model, some decisions are postponed until better information becomes available (e.g., an outcome of a random variable is realized), while other decisions must be made 'here and now.' For example, in a telecommunication network planning problem, decisions regarding the addition of network capacity have to be made before knowing customer demand (i.e., 'here and now'). Once the demand is realized, efficient usage of the network can then be determined. This work explores algorithms for the solution of such programs: stochastic linear programs with recourse. The algorithms investigated can be described as decomposition based cutting plane methods in which the cuts are estimated from random samples. Moreover, the algorithms all use the incremental sampling plan inherent to the Stochastic Decomposition (SD) algorithm developed by Higle and Sen in 1991. Our study includes both two stage and multistage programs. For the solution of two stage programs, we present the Conditional Stochastic Decomposition (CSD) algorithm, a multicut version of the SD algorithm. CSD is most suitable for situations in which data are difficult to obtain and may be computationally intense. Because of this potential intensity, we explore algorithms which require less computational effort than CSD. These algorithms combine features of both CSD and SD and are referred to as hybrid algorithms. Following our exploration of these algorithms for two stage problems, we next explore an extension of the SD algorithm that can be used for multistage problems with stagewise independent random variables. For the sake of notational brevity, our technical development is centered around the three stage case, although the extension to multistage problems is straightforward. Under mild conditions, convergence results similar to those found in the two stage algorithms hold. Multistage stochastic decomposition is currently a largely uncharted area. Our research represents the first major effort in this direction.
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Schmitz, Volker. "Copulas and stochastic processes." [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=972691669.
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Binotto, Giulia. "Contributions to stochastic analysis." Doctoral thesis, Universitat de Barcelona, 2018. http://hdl.handle.net/10803/565571.
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The aim of this dissertation is to present some new results on stochastic analysis. It consists on three works that deal with two Gaussian processes: the Brownian motion and the fractional Brownian motion with Hurst parameter H less than 1/2.
In the first work we construct a family of processes, from a single Poisson process and a sequence of independent random variables with common Bernoulli distribution, that converges in law to a complex Brownian motion. We find realizations of these processes that converge almost surely to the complex Brownian motion, uniformly on the unit time interval, and we derive the rate of convergence.
In the second work, we establish the weak convergence, in the topology of the Skorohod space, of the symmetric Riemann sums for functionals of the fractional Brownian motion when the Hurst parameter takes a critical value that depends on the chosen measure. As a consequence, we derive a change-of-variable formula in distribution, where the correction term is a stochastic integral with respect to a Brownian motion that is independent of the fractional Brownian motion.
The last work is devoted to prove that, when the delay goes to zero, the solution of delay differential equations driven by a Hölder continuous function of order in (1/3,1/2) converges with the supremum norm to the solution of the equation without delay.L’objectiu d’aquesta tesi és presentar alguns resultats innovadors en el camp de l’anàlisi estocàstica. Proposem tres treballs que tracten amb dos processos Gaussians: el moviment Brownià i el moviment Brownià fraccionari amb paràmetre de Hurst menor que 1/2. En el primer treball, construïm una família de processos, a partir d’un procés de Poisson i d’una seqüència de variables aleatòries independents amb distribució de Bernoulli, que convergeix en llei cap a un moviment Brownià complex. Trobem realitzacions d’aquests processos que convergeixen quasi segurament a un moviment Brownià complex, uniformement a l’interval de temps unitat. En derivem també la velocitat de convergència. En el segon treball, determinem la convergència feble, en la topologia de l’espai de Skorohod, de les sumes de Riemann simètriques per funcionals del moviment Brownià fraccionari quan el paràmetre de Hurst pren un valor crític que depèn de la mesura considerada. Com a conseqüència, derivem una fórmula de canvi de variable en distribució, on el terme de correcció és una integral estocàstica amb respecte a un moviment Brownià independent del moviment Brownià fraccionari. En l’últim treball demostrem que, quan el retard tendeix a zero, la solució d’equacions diferencials amb retard dirigides per una funció Hölder contínua amb ordre a (1/3,1/2) convergeix en la norma del suprem a la solució d’equacions sense retard.
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Gassmann, Horand Ingo. "Multi-period stochastic programming." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/27304.
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This dissertation presents various aspects of the solution of the linear multi-period stochastic programming problem. Under relatively mild assumptions on the structure of the random variables present in the problem, the value function at every time stage is shown to be jointly convex in the history of the process, namely the random variables observed so far as well as the decisions taken up to that point.
Convexity enables the construction of both upper and lower bounds on the value of the entire problem by suitable discretization of the random variables. These bounds are developed in Chapter 2, where it is also demonstrated how the bounds can be made arbitrarily sharp if the discretizations are chosen sufficiently fine. The chapter emphasizes computability of the bounds, but does not concern itself with finding the discretizations themselves.
The practise commonly followed to obtain a discretization of a random variable is to partition its support, usually into rectangular subsets. In order to apply the bounds of Chapter 2, one needs to determine the probability mass and weighted centroid for each element of the partition. This is a hard problem in itself, since in the continuous case it amounts to a multi-dimensional integration. Chapter 3 describes some Monte-Carlo techniques which can be used for normal distributions. These methods require random sampling, and the two main issues addressed are efficiency and accuracy. It turns out that the optimal method to use depends somewhat on the probability mass of the set in question.
Having obtained a suitable discretization, one can then solve the resulting large scale linear program which approximates the original problem. Its constraint matrix is highly structured, and Chapter 4 describes one algorithm which attempts to utilize this structure.
The algorithm uses the Dantzig-Wolfe decomposition principle, nesting decomposition
levels one inside the other. Many of the subproblems generated in the course of this decomposition share the same constraint matrices and can thus be solved simultaneously. Numerical results show that the algorithm may out-perform a linear programming package on some simple problems.
Chapter 5, finally, combines all these ideas and applies them to a problem in forest management. Here it is required to find logging levels in each of several time periods to maximize the expected revenue, computed as the volume cut times an appropriate discount factor. Uncertainty enters into the model in the form of the risk of forest fires and other environmental hazards, which may destroy a fraction of the existing forest. Several discretizations are used to formulate both upper and lower bound approximations to the original problem.Business, Sauder School of
Graduate
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Zangeneh, Bijan Z. "Semilinear stochastic evolution equations." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/31117.
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Let H be a separable Hilbert space. Suppose (Ω, F, Ft, P) is a complete stochastic basis with a right continuous filtration and {Wt,t ∈ R} is an H-valued cylindrical Brownian motion with respect to {Ω, F, Ft, P). U(t, s) denotes an almost strong evolution operator generated by a family of unbounded closed linear operators on H. Consider the semilinear stochastic integral equation
[formula omitted]
where
• f is of monotone type, i.e., ft(.) = f(t, w,.) : H → H is semimonotone, demicon-tinuous, uniformly bounded, and for each x ∈ H, ft(x) is a stochastic process which satisfies certain measurability conditions.
• gs(.) is a uniformly-Lipschitz predictable functional with values in the space of Hilbert-Schmidt operators on H.
• Vt is a cadlag adapted process with values in H.
• X₀ is a random variable.
We obtain existence, uniqueness, boundedness of the solution of this equation. We show the solution of this equation changes continuously when one or all of X₀, f, g, and V are varied. We apply this result to find stationary solutions of certain equations, and to study the associated large deviation principles.
Let {Zt,t ∈ R} be an H-valued semimartingale. We prove an Ito-type inequality and a Burkholder-type inequality for stochastic convolution [formula omitted]. These are the main tools for our study of the above stochastic integral equation.Science, Faculty of
Mathematics, Department of
Graduate