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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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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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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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Davies, M. J. "Topics in stochastic analysis". Thesis, Swansea University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636421.
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This thesis uses Nelson's stochastic mechanics to study a variety of problems. These include point sources, particles in a constant magnetic field with oscillator potentials and Brownian Motion with a constant drift. By using a finite difference approximation Chapter 1 gives an account of the Stochastic Variational Principle for stochastic mechanics based on Carlen's approach. It is shown that every diffusion satisfying the dynamical law of stochastic mechanics corresponds to a solution of the Schröinger equation. Chapter 2 is concerned with point sources and gives a brief account of Nelson's work in this field as well as examples of monochromatic one and two point particle sources as elucidated by Truman et al. The generator of the radial motion for a particle emitted by a point source is shown to be the generator of Brownian Motion with a constant drift. The transition density and expected first hitting times for this process are then derived explicitly. Chapter 3 gives a resuméof Shucker's result for sample paths of the Nelson stochastic process governed by the free wave function. Analogues of Shucker's result for the initial Gaussian wave function in the presence of a constant magnetic field together with positive or negative harmonic oscillator potentials are then proved. Finally Chapter 4 deals with the case of one dimensional Brownian Motion with a constant drift k on the half line (0,∞) with 0 accessible and ∞ inaccessible. Following some earlier work of Mandl the transition density for such a process is obtained explicitly for the most general boundary conditions leading to continuous sample paths and a contraction semigroup on C(0,∞) with generatorhskip 1.5cm. Usingvarious expectation values we obtain the distribution of first hitting times and last exit times for these processes.
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Nadakuditi, Rajesh Rao. "Applied stochastic Eigen-analysis". Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/38538.
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Thesis (Ph. D.)--Joint Program in Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science; and the Woods Hole Oceanographic Institution), 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Also issued in pages. Barker Engineering Library copy: issued in pages.
Includes bibliographical references (leaves 193-[201]).
The first part of the dissertation investigates the application of the theory of large random matrices to high-dimensional inference problems when the samples are drawn from a multivariate normal distribution. A longstanding problem in sensor array processing is addressed by designing an estimator for the number of signals in white noise that dramatically outperforms that proposed by Wax and Kailath. This methodology is extended to develop new parametric techniques for testing and estimation. Unlike techniques found in the literature, these exhibit robustness to high-dimensionality, sample size constraints and eigenvector misspecification. By interpreting the eigenvalues of the sample covariance matrix as an interacting particle system, the existence of a phase transition phenomenon in the largest ("signal") eigenvalue is derived using heuristic arguments. This exposes a fundamental limit on the identifiability of low-level signals due to sample size constraints when using the sample eigenvalues alone. The analysis is extended to address a problem in sensor array processing, posed by Baggeroer and Cox, on the distribution of the outputs of the Capon-MVDR beamformer when the sample covariance matrix is diagonally loaded.
(cont.) The second part of the dissertation investigates the limiting distribution of the eigenvalues and eigenvectors of a broader class of random matrices. A powerful method is proposed that expands the reach of the theory beyond the special cases of matrices with Gaussian entries; this simultaneously establishes a framework for computational (non-commutative) "free probability" theory. The class of "algebraic" random matrices is defined and the generators of this class are specified. Algebraicity of a random matrix sequence is shown to act as a certificate of the computability of the limiting eigenvalue distribution and, for a subclass, the limiting conditional "eigenvector distribution." The limiting moments of algebraic random matrix sequences, when they exist, are shown to satisfy a finite depth linear recursion so that they may often be efficiently enumerated in closed form. The method is applied to predict the deterioration in the quality of the sample eigenvectors of large algebraic empirical covariance matrices due to sample size constraints.
by Rajesh Rao Nadakuditi.
Ph.D.
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Liu, Xuan. "Some contribution to analysis and stochastic analysis". Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:485474c0-2501-4ef0-a0bc-492e5c6c9d62.
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The dissertation consists of two parts. The first part (Chapter 1 to 4) is on some contributions to the development of a non-linear analysis on the quintessential fractal set Sierpinski gasket and its probabilistic interpretation. The second part (Chapter 5) is on the asymptotic tail decays for suprema of stochastic processes satisfying certain conditional increment controls. Chapters 1, 2 and 3 are devoted to the establishment of a theory of backward problems for non-linear stochastic differential equations on the gasket, and to derive a probabilistic representation to some parabolic type partial differential equations on the gasket. In Chapter 2, using the theory of Markov processes, we derive the existence and uniqueness of solutions to backward stochastic differential equations driven by Brownian motion on the Sierpinski gasket, for which the major technical difficulty is the exponential integrability of quadratic processes of martingale additive functionals. A Feynman-Kac type representation is obtained as an application. In Chapter 3, we study the stochastic optimal control problems for which the system uncertainties come from Brownian motion on the gasket, and derive a stochastic maximum principle. It turns out that the necessary condition for optimal control problems on the gasket consists of two equations, in contrast to the classical result on ℝd, where the necessary condition is given by a single equation. The materials in Chapter 2 are based on a joint work with Zhongmin Qian (referenced in Chapter 2). Chapter 4 is devoted to the analytic study of some parabolic PDEs on the gasket. Using a new type of Sobolev inequality which involves singular measures developed in Section 4.2, we establish the existence and uniqueness of solutions to these PDEs, and derive the space-time regularity for solutions. As an interesting application of the results in Chapter 4 and the probabilistic representation developed in Chapter 2, we further study Burgers equations on the gasket, to which the space-time regularity for solutions is deduced. The materials in Chapter 4 are based on a joint work with Zhongmin Qian (referenced in Chapter 4). In Chapter 5, we consider a class of continuous stochastic processes which satisfy the conditional increment control condition. Typical examples include continuous martingales, fractional Brownian motions, and diffusions governed by SDEs. For such processes, we establish a Doob type maximal inequality. Under additional assumptions on the tail decays of their marginal distributions, we derive an estimate for the tail decay of the suprema (Theorem 5.3.2), which states that the suprema decays in a manner similar to the margins of the processes. In Section 5.4, as an application of Theorem 5.3.2, we derive the existence of strong solutions to a class of SDEs. The materials in this chapter is based on the work [44] by the author (Section 5.2 and Section 5.3) and an ongoing joint project with Guangyu Xi (Section 5.4).
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Johannessen, Knut. "Stochastic analysis of Workover Risers". Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for marin teknikk, 2010. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-11550.
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The goal of this thesis is to investigate the properties of dynamic analysis of slender, top tensioned risers when using both regular and irregular waves. The goal was to discover properties in the response that correlates to a parameter that can be found in both methods. The approach is to use a model of a riser in open water connected to the sea bed, and top tensioned by a semi submersible rig subjected to the dynamic load of waves and currents. The theories that hold the basis of dynamic analyses using finite elements are outlined, and different methods of solving the dynamic equilibrium equation are discussed. Relevant wave theories and their statistical properties are investigated and outlined, followed by a clear methodology for performing the case study. The data from the case study is based on a large number of irregular analyses, and one regular wave analysis for each sea state. The extreme values is extracted from the irregular simulations and fitted to a Gumbel extreme value distribution. The distributions are extrapolated to return periods of 1, 10 and 100 years, and compared to the extreme values from the regular wave analyses. The main results from the case study are: - The extreme response of an irregular simulation does not seem to correlate with the largest wave height in the simulation. - The bending moment seems to correlate weakly to the displacement and velocity of the rig. - The bending moment seems to correlate well with the displacement of the riser pipe. More in surge and pitch than in heave. - The bending moment seems to correlate well with the velocity of the riser pipe. More in surge and pitch than in heave. The results from the case study are used in a discussion on how to fine tune a regular wave analysis to be used in a consistent way to define the safe operation limitations for a top tensioned work over riser.
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Youssef, Nataly. "Stochastic analysis via robust optimization". Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/103246.
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Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2016.Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 167-174).
To evaluate the performance and optimize systems under uncertainty, two main avenues have been suggested in the literature: stochastic analysis and optimization describing the uncertainty probabilistically and robust optimization describing the uncertainty deterministically. Instead, we propose a novel paradigm which leverages the conclusions of probability theory and the tractability of the robust optimization approach to approximate and optimize the expected behavior in a given system. Our framework models the uncertainty via polyhedral sets inspired by the limit laws of probability. We characterize the uncertainty sets by variability parameters that we treat as random variables. We then devise a methodology to approximate and optimize the average performance of the system via a robust optimization formulation. Our framework (a) avoids the challenges of fitting probability distributions to the uncertain variables, (b) eliminates the need to generate scenarios to describe the states of randomness, and (c) demonstrates the use of robust optimization to evaluate and optimize expected performance. We illustrate the applicability of our methodology to analyze the performance of queueing networks and optimize the inventory policy for supply chain networks. In Part I, we study the case of a single queue. We develop a robust theory to study multi-server queues with possibly heavy-tailed primitives. Our methodology (a) provides approximations that match the diffusion approximations for light-tailed queues in heavy traffic, and (b) extends the framework to analyze the transient behavior of heavy-tailed queues. In Part II, we study the case of a network of queues. Our methodology provides accurate approximations of (a) the expected steady-state behavior in generalized queueing networks, and (b) the expected transient behavior in feedforward queueing networks. Our approach achieves significant computational tractability and provides accurate approximations relative to simulated values. In Part III, we study the case of a supply chain network. Our methodology (a) obtains optimal base-stock levels that match the optimal solutions obtained via stochastic optimization, (b) yields optimal affine policies which oftentimes exhibit better results compared to optimal base-stock policies, and (c) provides optimal policies that consistently outperform the solutions obtained via the traditional robust optimization approach.
by Nataly Youssef.
Ph. D.
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Whiteside, M. B. "Stochastic analysis of composite materials". Thesis, Imperial College London, 2012. http://hdl.handle.net/10044/1/9986.
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This thesis describes the development of stochastic analysis frameworks for use in engineering design and optimisation. The research focuses on fibre-reinforced composites, with the stochastic analyses of an existing analytical failure model for unidirectional composites and of a unit cell numerical model of a 2D 5-Harness satin weave. Stochastic failure envelopes are generated through parallelised Monte Carlo Simulation of deterministic, analytical, physically based failure criteria for unidirectional carbon fibre/epoxy matrix composite plies. Monte Carlo integration of global variance-based Sobol sensitivity indices is performed and utilised to decompose observed variance within stochastic failure envelopes into contributions from physical input parameters. It is observed how the interaction effect can be used to identify domains of bi-modal failure, within which the predicted failure probability is governed by multiple failure modes. A reduced unit cell (rUC) model of a 5-Harness satin weave is constructed and analysed deterministically in uniaxial and biaxial loading conditions. An algorithm is developed and implemented to fully automate the rUC construction such that stochastic variations of the crimp angle can be evaluated. Monte Carlo Simulation is employed to propagate the effect of the crimp angle through the deterministic model and the probabilistic response compared with data obtained experimentally. It is observed how simulated variability compares well in uni-axial compression, but under-predicts observed experimental variability in uni-axial tension. The influence of vertical stacking sequence of plies is also demonstrated through the study of in-phase and out-of-phase periodic boundary conditions. The research highlights various, potential advantages that stochastic methodologies offer over the traditional deterministic approach, making a case for their application in engineering design and providing a springboard for further research come the day when greater computational power is available.
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Güngör, Mesut Savacı Ferit Acar. "Analysis of Stochastic Dynamical Systems/". [s.l.]: [s.n.], 2007. http://library.iyte.edu.tr/tezler/master/elektrikveelektronikmuh/T000630.pdf.
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Labeodan, Moremi Morire OreOluwapo. "Stochastic analysis of AIDS epidemiology". Thesis, Pretoria : [s.l.], 2009. http://upetd.up.ac.za/thesis/available/etd-10172009-112824.
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Prömel, David Johannes. "Robust stochastic analysis with applications". Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://dx.doi.org/10.18452/17373.
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Diese Dissertation präsentiert neue Techniken der Integration für verschiedene Probleme der Finanzmathematik und einige Anwendungen in der Wahrscheinlichkeitstheorie. Zu Beginn entwickeln wir zwei Zugänge zur robusten stochastischen Integration. Der erste, ähnlich der Ito’schen Integration, basiert auf einer Topologie, erzeugt durch ein äußeres Maß, gegeben durch einen minimalen Superreplikationspreis. Der zweite gründet auf der Integrationtheorie für rauhe Pfade. Wir zeigen, dass das entsprechende Integral als Grenzwert von nicht antizipierenden Riemannsummen existiert und dass sich jedem "typischen Preispfad" ein rauher Pfad im Ito’schen Sinne zuordnen lässt. Für eindimensionale "typische Preispfade" wird sogar gezeigt, dass sie Hölder-stetige Lokalzeiten besitzen. Zudem erhalten wir Verallgemeinerungen von Föllmer’s pfadweiser Ito-Formel. Die Integrationstheorie für rauhe Pfade kann mit dem Konzept der kontrollierten Pfade und einer Topologie, welche die Information der Levy-Fläche enthält, entwickelt werden. Deshalb untersuchen wir hinreichende Bedingungen an die Kontrollstruktur für die Existenz der Levy-Fläche. Dies führt uns zur Untersuchung von Föllmer’s Ito-Formel aus der Sicht kontrollierter Pfade. Para-kontrollierte Distributionen, kürzlich von Gubinelli, Imkeller und Perkowski eingeführt, erweitern die Theorie rauher Pfade auf den Bereich von mehr-dimensionale Parameter. Wir verallgemeinern diesen Ansatz von Hölder’schen auf Besov-Räume, um rauhe Differentialgleichungen zu lösen, und wenden die Ergebnisse auf stochastische Differentialgleichungen an. Zum Schluß betrachten wir stark gekoppelte Systeme von stochastischen Vorwärts-Rückwärts-Differentialgleichungen (FBSDEs) und erweitern die Theorie der Existenz, Eindeutigkeit und Regularität der sogenannten Entkopplungsfelder auf Markovsche FBSDEs mit lokal Lipschitz-stetigen Koeffizienten. Als Anwendung wird das Skorokhodsche Einbettungsproblem für Gaußsche Prozesse mit nichtlinearem Drift gelöst.In this thesis new robust integration techniques, which are suitable for various problems from stochastic analysis and mathematical finance, as well as some applications are presented. We begin with two different approaches to stochastic integration in robust financial mathematics. The first one is inspired by Ito’s integration and based on a certain topology induced by an outer measure corresponding to a minimal superhedging price. The second approach relies on the controlled rough path integral. We prove that this integral is the limit of non-anticipating Riemann sums and that every "typical price path" has an associated Ito rough path. For one-dimensional "typical price paths" it is further shown that they possess Hölder continuous local times. Additionally, we provide various generalizations of Föllmer’s pathwise Ito formula. Recalling that rough path theory can be developed using the concept of controlled paths and with a topology including the information of Levy’s area, sufficient conditions for the pathwise existence of Levy’s area are provided in terms of being controlled. This leads us to study Föllmer’s pathwise Ito formulas from the perspective of controlled paths. A multi-parameter extension to rough path theory is the paracontrolled distribution approach, recently introduced by Gubinelli, Imkeller and Perkowski. We generalize their approach from Hölder spaces to Besov spaces to solve rough differential equations. As an application we deal with stochastic differential equations driven by random functions. Finally, considering strongly coupled systems of forward and backward stochastic differential equations (FBSDEs), we extend the existence, uniqueness and regularity theory of so-called decoupling fields to Markovian FBSDEs with locally Lipschitz continuous coefficients. These results allow to solve the Skorokhod embedding problem for a class of Gaussian processes with non-linear drift.
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Wu, Ling. "Stochastic Modeling and Statistical Analysis". Scholar Commons, 2010. https://scholarcommons.usf.edu/etd/1813.
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The objective of the present study is to investigate option pricing and forecasting problems in finance. This is achieved by developing stochastic models in the framework of classical modeling approach.
In this study, by utilizing the stock price data, we examine the correctness of the existing Geometric Brownian Motion (GBM) model under standard statistical tests. By recognizing the problems, we attempted to demonstrate the development of modified linear models under different data partitioning processes with or without jumps. Empirical comparisons between the constructed and GBM models are outlined.
By analyzing the residual errors, we observed the nonlinearity in the data set. In order to incorporate this nonlinearity, we further employed the classical model building approach to develop nonlinear stochastic models. Based on the nature of the problems and the knowledge of existing nonlinear models, three different nonlinear stochastic models are proposed. Furthermore, under different data partitioning processes with equal and unequal intervals, a few modified nonlinear models are developed. Again, empirical comparisons between the constructed nonlinear stochastic and GBM models in the context of three data sets are outlined.
Stochastic dynamic models are also used to predict the future dynamic state of processes. This is achieved by modifying the nonlinear stochastic models from constant to time varying coefficients, and then time series models are constructed. Using these constructed time series models, the prediction and comparison problems with the existing time series models are analyzed in the context of three data sets. The study shows that the nonlinear stochastic model 2 with time varying coefficients is robust with respect different data sets.
We derive the option pricing formula in the context of three nonlinear stochastic models with time varying coefficients. The option pricing formula in the frame work of hybrid systems, namely, Hybrid GBM (HGBM) and hybrid nonlinear stochastic models are also initiated.
Finally, based on our initial investigation about the significance of presented nonlinear stochastic models in forecasting and option pricing problems, we propose to continue and further explore our study in the context of nonlinear stochastic hybrid modeling approach.
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Tsang, Wai-yin, i 曾慧賢. "Aspects of modelling stochastic volatility". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31223515.
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Tsang, Wai-yin. "Aspects of modelling stochastic volatility /". Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22078952.
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Wang, Zimeng. "Stochastic optimal controls with delay". Thesis, University of Nottingham, 2017. http://eprints.nottingham.ac.uk/47816/.
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This thesis investigates stochastic optimal control problems with discrete delay and those with both discrete and exponential moving average delays, using the stochastic maximum principle, together with the methods of conjugate duality and dynamic programming. To obtain the stochastic maximum principle, we first extend the conjugate duality method presented in [2, 44] to study a stochastic convex (primal) problem with discrete delay. An expression for the corresponding dual problem, as well as the necessary and sufficient conditions for optimality of both problems, are derived. The novelty of our work is that, after reformulating a stochastic optimal control problem with delay as a particular convex problem, the conditions for optimality of convex problems lead to the stochastic maximum principle for the control problem. In particular, if the control problem involves both the types of delay and is jump-free, the stochastic maximum principle obtained in this thesis improves those obtained in [29, 30]. Adapting the technique used in [19, Chapter 3] to the stochastic context, we consider a class of stochastic optimal control problems with delay where the value functions are separable, i.e. can be expressed in terms of so-called auxiliary functions. The technique enables us to obtain second-order partial differential equations, satisfied by the auxiliary functions, which we shall call auxiliary HJB equations. Also, the corresponding verification theorem is obtained. If both the types of delay are involved, our auxiliary HJB equations generalize the HJB equations obtained in [22, 23] and our verification theorem improves the stochastic verification theorem there.
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Bakhtiari, Siamak. "Stochastic finite element slope stability analysis". Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/stochastic-finite-element-slope-stability-analysis(c1b451d9-8bf6-43ff-9c10-7b5209fb45c1).html.
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In this thesis, the failures that occurred during the construction of the Jamuna Bridge Abutment in Bangladesh have been investigated. In particular, the influence of heterogeneity on slope stability has been studied using statistical methods, random field theory and the finite element method. The research is divided into three main parts: the statistical characterization of the Jamuna River Sand, based on an extensive in-situ and laboratory database available for the site; calibration of the laboratory data against a double-hardening elastoplastic soil model; and stochastic finite element slope stability analyses, using a Monte Carlo simulation, to analyse the slope failures accounting for heterogeneity. The sand state has been characterised in terms of state parameter, a meaningful quantity which can fully represent the mechanical behaviour of the soil. It was found that the site consists of predominantly loose to mildly dilative material and is very variable. Also, a Normal distribution was found to best represent the state parameter and a Lognormal distribution was found to best represent the tip resistance.The calibration of the constitutive model parameters was found to be challenging, as alternative approaches had to be adopted due to lack of appropriate test results available for the site. Single-variate random fields of state parameter were then linked to the constitutive model parameters based on the relationships found between them, and a parametric study of the abutment was then carried out by linking finite elements and random field theory within a Monte Carlo framework.It was found that, as the degree of anisotropy of the heterogeneity increases, the range of structural responses increases as well. For the isotropic cases, the range of responses was relatively smaller and tended to result in more localised failures. For the anisotropic cases, it was found that there are two different types of deformation mechanism. It was also found that, as the vertical scale of fluctuation becomes bigger, the range of possible structural responses increases and failure is more likely. Finally, it was found that the failed zones observed during the excavation of the West Guide Bund of the Jamuna Bridge Abutment could be closely predicted if heterogeneity was considered in the finite element analyses. In particular, it was found that, for such a natural deposit, a large degree of anisotropy (in the range of 20) could account for the deformation mechanisms observed on site.
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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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Fahlberg-Stojanovska, Linda Dianne. "Stochastic stability of Lozi mappings". Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184748.
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We study the Lozi mapping f(x,y) = (1+by-a|x|,x) acting on a compact trapping region in R² and prove that its Sinai-Bowen-Ruelle measure is stable under small random perturbations. This extends the results of Kifer and Young [Y2] for Axiom A attractors to a piecewise hyperbolic setting.
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Fashandi, Ali R. M. "Stochastic analysis of robot-safety systems". Thesis, University of Ottawa (Canada), 1998. http://hdl.handle.net/10393/4112.
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Robot population is increasing at an incredible pace. Over the last fifteen years, robot population grew from 30,000 in 1983, to the forecasted 820,000 by the end of 1998. Their infancy period has come to an end and they are not just being used in the automotive industry or required to perform simple tasks. They are now being employed in various sectors of industry and handle much more complex operations. Increased robot system complexity and their critical applications utilization have led to various reliability and safety problems. In 1982, the Machine Tool Trade Associations guidelines stated that a working robot can be a potential hazard to personnel under certain circumstances. The need for robot system safety was highlighted by a 10-million dollar lawsuit awarded to the family of a worker killed by an industrial robot in 1983. This study presents a detailed introductory aspect of robot safety, an identification of the most appropriate robot systems reliability and safety assessment techniques, and probabilistic modelling of robot-safety systems. The domain of the probabilistic models include: a stochastic analysis of a system containing one robot with n-redundant safety units, a stochastic analysis of a system composed of n-redundant robots with one safety unit, and an availability analysis of robot systems susceptible to common-cause failure. The primal intent of the analyses is to develop generalized and numerical expressions relating to the performance indices for robot systems operating with or without the safety unit. Generalized models are introduced and generalized expressions including reliability, time-dependent availability, steady-state availability, and mean time to failure (MTTF) are developed. In order to assess performance indices, some special cases of the generalized models are presented resulting in the formation of numerical values. Robot system performance indices are determined by means of the Markovian and non-Markovian methods. The method of supplementary variables and the device of stages are used to deal with the non-Markovian models. Various failed system repair time distributions (i.e., exponential, gamma, Weibull, Rayleigh, and log-normal distributions) have been considered to obtain generalized steady state availability expressions. Markov method is utilized in models where failure and repair rates are assumed constant. With the aid of Laplace transforms, a system of first-order differential equations are solved and generalized reliability and MTTF expressions are developed.
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Satish, Shah Aashish. "Stochastic analysis of human-machine systems". Thesis, University of Ottawa (Canada), 2006. http://hdl.handle.net/10393/27175.
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This study presents a stochastic analysis of three-state device systems subjected to critical human errors and common-cause failures. The systems analysed incorporate elements of commonly used redundant configurations such as parallel, series, k-out-of-n and standby. For the systems that are subjected to constant failure and repair rates, the Markov State Space technique is used to perform the reliability and availability analysis. Generalized and special-case expressions for the system reliability, the mean time to failure, the steady state availability and the time-dependent availability for each of these systems are developed. For the parallel system with non-constant failure and repair rates, the Device of Stages approach is used to formulate a modified Markov model with the addition of dummy states. The impact of human error, common-cause failure, failed system repair policy and elements of redundant configurations on the values of the system reliability, the mean time to failure, the time-dependent availability and the steady state availability is demonstrated by means of plots. (Abstract shortened by UMI.)
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Mahmoudi, Fashandi Ali R. "Stochastic analysis of robot-safety systems". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape17/PQDD_0026/NQ36781.pdf.
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Roelly, Sylvie. "Reciprocal processes : a stochastic analysis approach". Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6458/.
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Reciprocal processes, whose concept can be traced back to E. Schrödinger,
form a class of stochastic processes constructed as mixture of bridges, that satisfy a time Markov field property. We discuss here a new unifying approach to characterize several types of reciprocal processes via duality formulae on path spaces: The case of reciprocal processes with continuous paths associated to Brownian diffusions and the case of pure jump reciprocal processes associated to counting processes are treated. This presentation is based on joint works with M. Thieullen, R. Murr and C. Léonard.
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Waddington, Jonathan. "Human optokinetic nystagmus : a stochastic analysis". Thesis, University of Plymouth, 2012. http://hdl.handle.net/10026.1/1040.
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Optokinetic nystagmus (OKN) is a fundamental gaze-stabilising response in which eye movements attempt to compensate for the retinal slip caused by self-motion. The OKN response consists of a slow following movement made in the direction of stimulus motion interrupted by fast eye movements that are primarily made in the opposite direction. The timing and amplitude of these slow phases and quick phases are notably variable, but this variability is poorly understood. In this study I performed principal component analysis on OKN parameters in order to investigate how the eigenvectors and eigenvalues of the underlying components contribute to the correlation between OKN parameters over time. I found three categories of principal components that could explain the variance within each cycle of OKN, and only parameters from within a single cycle contributed highly to any given component. Differences found in the correlation matrices of OKN parameters appear to reflect changes in the eigenvalues of components, while eigenvectors remain predominantly similar across participants, and trials. I have developed a linear and stochastic model of OKN based on these results and demonstrated that OKN can be described as a 1st order Markov process, with three sources of noise affecting SP velocity, QP triggering, and QP amplitude. I have used this model to make some important predictions about the optokinetic reflex: the transient response of SP velocity, the existence of signal dependent noise in the system, the target position of QPs, and the threshold at which QPs are generated. Finally, I investigate whether the significant variability within OKN may represent adaptive control of explicit and implicit parameters. iii
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Wei, Xiaofan. "Stochastic Analysis and Optimization of Structures". University of Akron / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=akron1163789451.
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Salikhova, Alsu <1982>. "Stochastic Volatility Analysis for Hedge Funds". Master's Degree Thesis, Università Ca' Foscari Venezia, 2013. http://hdl.handle.net/10579/3351.
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Chugreeva, Olga [Verfasser], Christof Erich [Akademischer Betreuer] Melcher i 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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Sorensen, Julian Karl. "White noise analysis and stochastic evolution equations". Title page, contents and abstract only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phs713.pdf.
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Ramos, José A. "A stochastic realization and model reduction approach to streamflow modeling". Diss., Georgia Institute of Technology, 1985. http://hdl.handle.net/1853/32869.
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Sun, Junfeng. "Stochastic models for compliance analysis and applications". Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1117049743.
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Meng, Yu. "Bayesian Analysis of a Stochastic Volatility Model". Thesis, Uppsala University, Department of Mathematics, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-119972.
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Eliiyi, Ugur. "Discrete-time Stochastic Analysis Of Land Combat". Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/759472/index.pdf.
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In this study, we present the implementation and experimental analysis of a modeling approach for analyzing tactical level land combat to generate information for weapon and ammunition planning. The discrete-time stochastic model (DSM), which can handle small and moderately large force levels, is based on single shot kill probabilities. Forces are assumed to be heterogeneous on both sides, and both directed and area fire types are modeled by means of combinatorial analysis. DSM considers overkills and can handle noncombat loss and engagement processes, discrete reinforcements, force combinations and divisions. In addition to experimenting with DSM, we estimate attrition rate coefficients used in Lanchester combat models, such that the two models will yield similar figures for force levels throughout the combat.
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Hwisu, Shin. "Stochastic Analysis For Water Pipeline System Management". 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/202696.
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Subramanian, Parmeshwar. "The stochastic analysis of technical redundant systems". Thesis, University of Ottawa (Canada), 2001. http://hdl.handle.net/10393/6066.
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Today computers are widely used and their failures can lead to catastrophe. Redundancy is used to improve computer system reliability. This study presents a qualitative analysis of triple modular redundant (TMR) systems with redundant voters that can help to reduce the risk of failures. The voters examine the output of triple modular systems. Markov technique was employed to perform the analysis. Generalized formulas for reliability and mean time to failures of TMR systems with N voters have been developed. In addition, the system state probabilities in s-domain and steady state probabilities have been presented. The study clearly demonstrates improvements in system reliability, mean time to failure and steady state availability by the introduction of repair and redundancy in these systems.
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Cheng, Shen. "Stochastic analysis of standby robot-safety systems". Thesis, University of Ottawa (Canada), 2007. http://hdl.handle.net/10393/27820.
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Nowadays, the application of robots covers almost all aspects of our daily life. They are used to perform increasing complex and critical operations. The increased critical applications have led to various reliability and safety problems, especially many people are injured and killed every year.
This study presents reliability and availability analyses of six different standby robot-safety systems: one robot and (n-1) standby safety units with a perfect switch, one robot and (n-1) standby safety units with an imperfect switch, (n-1) standby robots and one safety unit with a perfect switch, (n-1) standby robots and one safety unit with an imperfect switch, n parallel robots and (m-1) standby unit with a perfect switch, and two parallel robots and one standby unit with an imperfect switch.
With the aid of Markov and supplementary variable methods, general expressions for system state probabilities, system availability, reliability and mean time to failure were obtained. Plots of some of these expressions are shown to demonstrate the effect of varying failure rates or repair rates of the safety unit, and other parameters.
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Bréhier, Charles-Edouard. "Numerical analysis of highly oscillatory Stochastic PDEs". Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2012. http://tel.archives-ouvertes.fr/tel-00824693.
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In a first part, we are interested in the behavior of a system of Stochastic PDEs with two time-scales- more precisely, we focus on the approximation of the slow component thanks to an efficient numerical scheme. We first prove an averaging principle, which states that the slow component converges to the solution of the so-called averaged equation. We then show that a numerical scheme of Euler type provides a good approximation of an unknown coefficient appearing in the averaged equation. Finally, we build and we analyze a discretization scheme based on the previous results, according to the HMM methodology (Heterogeneous Multiscale Method). We precise the orders of convergence with respect to the time-scale parameter and to the parameters of the numerical discretization- we study the convergence in a strong sense - approximation of the trajectories - and in a weak sense - approximation of the laws. In a second part, we study a method for approximating solutions of parabolic PDEs, which combines a semi-lagrangian approach and a Monte-Carlo discretization. We first show in a simplified situation that the variance depends on the discretization steps. We then provide numerical simulations of solutions, in order to show some possible applications of such a method.
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Zeryos, Mihail. "Bayesian pursuit analysis and singular stochastic control". Thesis, Imperial College London, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338932.
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Tribastone, Mirco. "Scalable analysis of stochastic process algebra models". Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4629.
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The performance modelling of large-scale systems using discrete-state approaches is fundamentally hampered by the well-known problem of state-space explosion, which causes exponential growth of the reachable state space as a function of the number of the components which constitute the model. Because they are mapped onto continuous-time Markov chains (CTMCs), models described in the stochastic process algebra PEPA are no exception. This thesis presents a deterministic continuous-state semantics of PEPA which employs ordinary differential equations (ODEs) as the underlying mathematics for the performance evaluation. This is suitable for models consisting of large numbers of replicated components, as the ODE problem size is insensitive to the actual population levels of the system under study. Furthermore, the ODE is given an interpretation as the fluid limit of a properly defined CTMC model when the initial population levels go to infinity. This framework allows the use of existing results which give error bounds to assess the quality of the differential approximation. The computation of performance indices such as throughput, utilisation, and average response time are interpreted deterministically as functions of the ODE solution and are related to corresponding reward structures in the Markovian setting. The differential interpretation of PEPA provides a framework that is conceptually analogous to established approximation methods in queueing networks based on meanvalue analysis, as both approaches aim at reducing the computational cost of the analysis by providing estimates for the expected values of the performance metrics of interest. The relationship between these two techniques is examined in more detail in a comparison between PEPA and the Layered Queueing Network (LQN) model. General patterns of translation of LQN elements into corresponding PEPA components are applied to a substantial case study of a distributed computer system. This model is analysed using stochastic simulation to gauge the soundness of the translation. Furthermore, it is subjected to a series of numerical tests to compare execution runtimes and accuracy of the PEPA differential analysis against the LQN mean-value approximation method. Finally, this thesis discusses the major elements concerning the development of a software toolkit, the PEPA Eclipse Plug-in, which offers a comprehensive modelling environment for PEPA, including modules for static analysis, explicit state-space exploration, numerical solution of the steady-state equilibrium of the Markov chain, stochastic simulation, the differential analysis approach herein presented, and a graphical framework for model editing and visualisation of performance evaluation results.
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Dehmeshki, Jamshid. "Stochastic model-based approach to image analysis". Thesis, University of Nottingham, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.363908.
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Shi, Fangwei. "Asymptotic analysis of new stochastic volatility models". Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/60648.
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A good options pricing model should be able to fit the market volatility surface with high accuracy. While the standard continuous stochastic volatility models can generate volatility smiles consistent with market data for relatively larger maturities, these models cannot reproduce market smiles for small maturities, which have the well-observed 'small-time explosion' feature. In this thesis we propose three new types of stochastic volatility models, and we focus on the small-time asymptotic behaviour of the implied volatility in these models. We show that these models can generate implied volatilities with explosion, hence they can theoretically provide a better fit to the market data. The thesis is organised as follows. Chapter 0 is the introduction. We briefly discuss the development and performance of standard continuous stochastic volatility models, and raise the small-time fitness issue of these traditional models. In Chapter 1 we propose the randomised Heston model and analyse its small and large time asymptotic behaviours. In particular, we show that any small-time explosion rate in between of [0, 1/2] for the implied variance can be captured by a suitable choice of the initial randomisation. In Chapter 2 we propose a fractional version of the Heston model and detail the small-time asymptotic behaviour of the implied volatility in this setting. We precise the link between the explosion rate and the Hurst parameter. Finally, in Chapter 3 we propose a new stochastic volatility model based on the recent work by Conus and Wildman in which the stock price can have past dependency. We show that in the case of a CIR variance process this model has similar behaviours to a fractional Heston environment.
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Wiley, Richard Paul. "Performance analysis of Stochastic Timed Petri Nets". Thesis, Massachusetts Institute of Technology, 1985. http://hdl.handle.net/1721.1/15002.
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Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1986.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING
Bibliography: leaves 305-310.
by Richard Paul Wiley.
Sc.D.
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Graham, D. P. "Stochastic modelling and analysis of construction processes". Thesis, University of Edinburgh, 2005. http://hdl.handle.net/1842/12054.
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Construction projects frequently overrun and finish over budget; in part due to the lack of control that construction practitioners have over the construction schedule at a process level. Planning methods such as CPM are not of sufficient detail to allow a practitioner to plan a process to maximise its performance. Thus the aim of this research was to develop a practical, computer-based model to enable practitioners to plan projects at a process level and hence improve their projects. This research has focused upon a specific type of process - those that are stochastic and cyclical. Such processes are difficult to predict and hence control, and they are widespread throughout construction projects. Examples are crane operations, formwork erection and scaffold erection. Initially, a focus was placed on the ready-mixed concrete (RMC) supply process. A discrete event simulation (DES) model of this process was developed and validated, based upon real project data. This model could not provide accurate estimates of the process due to the requirement that a user define the probability distributions that represent the process. This is a complex requirement for a practitioner, the issue became known as the complexity problem and a solution was sought using case-based reasoning (CBR). CBR provides solutions to new problems using knowledge from past ones - exactly what a practitioner was doing in the above simulation model. CBR was shown to be capable of solving the complexity problem. A hybrid model, CBRSim, was formed to fulfil the original aim of this thesis. CBRSim works by: CBR selecting probability distributions (based on user input) that are used in a DES model to accurately recreate the process. CBRSim was validated and modelled the process to within +/- 3% accuracy. CBRSim was then applied to another stochastic and cyclical construction process: earthmoving. CBRSim was found to be more accurate in estimating earthmoving productivity than RMC supply, thus providing an indication of a generic modelling capability.
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Maglaras, George K. "Integrated analysis and design in stochastic optimization". Thesis, Virginia Tech, 1989. http://hdl.handle.net/10919/46048.
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When structural optimization is performed via an iterative solution technique, it is possible to integrate the analysis and design iterations, in an integrated analysis and design procedure. The present work seeks to apply an integrated analysis and design approach in reliability based optimization, when a safety index approach is used.
Two variants of the new approach are presented. Both of them are based on partially converged solution of the optimization procedure. The safety index approach employed allows us to use semi-analytical formulas to calculate the sensitivity derivatives of the safety constraints.
The new approach is applied to the design of a simple structure. Both methods are robust to a satisfactory degree. The results are compared to those obtained by the safety index approach without integrating the analysis and design processes. The new methods substantially reduce the computational cost of optimization, which indicates that integrated analysis and design has the potential of removing a major obstacle, which is the excessive computational cost, in applying stochastic optimization to real life structural design.
Master of Science
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Cash, Charles R. "Stochastic Analysis of Multi-Item Flow Lines /". The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487931993468164.
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Cao, Fengming. "Network system performance analysis with stochastic geometry". Thesis, University of Bristol, 2017. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707760.
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Zaidi, Syed Ali Raza. "Stochastic geometric analysis of cognitive wireless networks". Thesis, University of Leeds, 2013. http://etheses.whiterose.ac.uk/5490/.
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The prime objective of this thesis is to study these interference management mechanisms for quantifying the potential gains of CRs in terms of spectral utility. Interference modeling is the most important aspect of this extensive evaluation. Accurate modeling of the cognitive network interference, accommodating its stochastic nature (triggered by both spatial and propagation dynamics) is therefore a central contribution of this thesis. Since the aggregate interference from CRs is a function of the access strategy, two wellknown access paradigms, namely, spectrum underlay and interweave, are thoroughly analyzed. For the spectrum underlay access mechanism, a guard-zone based interference control mechanism is examined. Specifically, CRs are obliged to maintain silence in a spatial no-talk zone of a certain radius which is centered on a primary receiver. It is shown that the radius of the guard-zone is strongly coupled with the medium access and routing strategies employed by the CRs. While the guard-zone provides a robust mechanism to protect a single primary user, it is a challenging task to achieve the same for a large scale primary network. An alternative degree of freedom, i.e., medium access probability (MAP), can easily address this issue. Furthermore, for a large CR network (CRN), significant gains can be harnessed by furnishing nodes with multiple antennas. Performance evaluation of such a network with MAP adaptation is one of the key contributions of this dissertation. It is shown that the multi-antenna paradigm results in a “win-win” situation for both primary and secondary users. In order to facilitate multi-hop communication between CRs, a quality-of-service (QoS) aware routing is also devised. We show that there exists an optimal MAP which maximizes the spectral utility of the secondary network. However, such an optimal point often lies outside the permissible operational regime dictated by the primary user’s co-existence constraint. Another approach can be adopted where we exploit a different degree of freedom, i.e., the transmit power employed by the CRs. Thus CRs can extend their operational regime by adapting one degree of freedom and selecting an optimal value for another. The optimality of this adapt-and-optimize strategy is shown for a variety of networking paradigms. Finally, the performance of the primary user in the presence of the interference-channel-aware CRs is quantified. For a CRN employing an interweave configuration, the performance of a legacy user is investigated. The impact of different network parameters is explored. It is shown that the cooperation between the CR transmitter and receiver can significantly improve the performance of the interference avoidance mechanism. Furthermore,we highlight that ignoring the self-coexistence criteria for the secondary network leads to an over-estimation of the aggregate interference and consequently results in pessimistic design strategies. The analysis is extended to consider the performance of a large primary network. Finally, a novel modification in the analytical approach is proposed so that performance guarantees can be provided to the existing users. Another contribution of this dissertation is to evaluate (currently very topical and very important) the energy efficiency of an ad hoc wireless network. The key motivation is to investigate the impact of the co-channel interference on the network-wide energy consumption. Both energy and spectral efficiency problems have a common origin, i.e., growing bandwidth demand. Also the design of both problems require understanding of co-channel interference management strategies. Finally,we try to put pull together all the analysis and simulation results to look at both open problems and directions for future research in this highly topical, and strategically important research areas of enabling high speed, future wireless networks.
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Pahle, Jürgen. "Stochastic simulation and analysis of biochemical networks". Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2008. http://dx.doi.org/10.18452/15786.
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Stochastische Effekte können einen großen Einfluss auf die Funktionsweise von biochemischen Netzwerken haben. Vor allem Signalwege, z.B. Calciumsignaltransduktion, sind anfällig gegenüber zufälligen Schwankungen. Daher stellt sich die wichtige Frage, wie dadurch der Informationstransfer in diesen Systemen beeinträchtigt wird. Zunächst werden eine Reihe von stochastischen Simulationsmethoden diskutiert und systematisch klassifiziert. Dies dient als methodische Grundlage der ganzen Dissertation. Der Schwerpunkt liegt hier auf approximativen und hybriden Ansätzen, einschließlich der Hybridmethode des Softwaresystems Copasi, deren Implementierung Teil dieser Arbeit war. Die Dynamik biochemischer Systeme zeigt in den meisten Fällen einen Übergang von stochastischem zu deterministischem Verhalten mit steigender Partikelzahl. Dieser Übergang wird für Calciumsignaltransduktion und andere Systeme untersucht. Es zeigt sich, dass das Auftreten stochastischer Effekte stark von der Sensitivität des Systems abhängt. Ein Maß dafür ist die Divergenz. Systeme mit hoher Divergenz zeigen noch mit hohen Teilchenzahlen stochastische Effekte und umgekehrt. Schließlich wird der Einfluss von zufälligen Fluktuationen auf die Leistungsfähigkeit von Signalpfaden erforscht. Dazu werden simulierte sowie experimentell gemessene Calcium-Zeitreihen stochastisch an die Aktivierung eines Zielenzyms gekoppelt. Das Schätzen des informationstheoretischen Maßes Transferentropie unter unterschiedlichen zellulären Bedingungen dient zur Abschätzung des Informationstransfers. Dieser nimmt mit steigender Partikelzahl zu, ist jedoch sehr abhängig von der momentanen Dynamik (z.B. spikende, burstende oder irreguläre Oszillationen). Die hier entwickelten Methoden, wie der Gebrauch der Divergenz als Indikator für den stoch./det. Übergang oder die stochastische Kopplung und informationstheoretische Analyse mittels Transferentropie, sind wertvolle Werkzeuge für die Analyse von biochemischen Systemen.Stochastic effects in biochemical networks can affect the functioning of these systems significantly. Signaling pathways, such as calcium signal transduction, are particularly prone to random fluctuations. Thus, an important question is how this influences the information transfer in these pathways. First, a comprehensive overview and systematic classification of stochastic simulation methods is given as methodical basis for the thesis. Here, the focus is on approximate and hybrid approaches. Also, the hybrid solver in the software system Copasi is described whose implementation was part of this PhD work. Then, in most cases, the dynamic behavior of biochemical systems shows a transition from stochastic to deterministic behavior with increasing particle numbers. This transition is studied in calcium signaling as well as other test systems. It turns out that the onset of stochastic effects is very dependent on the sensitivity of the specific system quantified by its divergence. Systems with high divergence show stochastic effects even with high particle numbers and vice versa. Finally, the influence of noise on the performance of signaling pathways is investigated. Simulated and experimentally measured calcium time series are stochastically coupled to an intracellular target enzyme activation process. Then, the information transfer under different cellular conditions is estimated with the information-theoretic quantity transfer entropy. The amount of information that can be transferred increases with rising particle numbers. However, this increase is very dependent on the current dynamical mode of the system, such as spiking, bursting or irregular oscillations. The methods developed in this thesis, such as the use of the divergence as an indicator for the transition from stochastic to deterministic behavior or the stochastic coupling and information-theoretic analysis using transfer entropy, are valuable tools for the analysis of biochemical systems.
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McVinish, Ross Stewart. "Stochastic analysis and approximation of fractional diffusion". Thesis, Queensland University of Technology, 2002.
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Manica, Nicola. "Stochastic Analysis of a resource reservation system". Doctoral thesis, Università degli studi di Trento, 2013. https://hdl.handle.net/11572/367896.
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An unmistakable trend in embedded systems is the growth of
soft real-time computing. A soft real-time application is one for which deadlines can occasionally be missed, but the probability of this event has to be controllable and predictable.
This work is aimed to close the gap in the research of stochastic real-time analysis related to resource reservation scheduling algorithms. This dissertation attempts to:
1. give a quick overview of classic real-time analysis
2. analyze the problems related to use the well-known techniques in the context of soft real-time applications:
• overvalue the assignation of parameters as in hard real-
time systems based on worst case execution times
• time and memory complexity using the known theoretical
stochastic analysis
3. propose solutions able to overcome the limitation showed in point 2
4. show some specific examples (theoretical and practical) in which resource reservation lead to advantages.
The novel contributions of this thesis are:
• a new bound to predict the probability of a deadline misses in a resource reservation systems
• a very efficient numeric solution for matrix generated with well-know abstraction models of reservation based on Quasi Birth Death Markov Process
• an analytical solution, with some conservative approximations, for the same models.
• a new model for specific applications, like interrupts.
• experiments using resource reservation in different contexts
The thesis is evolved following two different approaches:
1. the first based on the exact model of reservation, and the contributions is:
• define a new pessimistic bound, efficient in term of computation, able to overcome the problem of complete knowledge of the computation time. The solution is an approximation of the real solution of the model.
2. the second based on an approximation model in which the
novel contributions are:
• presents an exact and numeric efficient solution for the
model based on Quasi Birth and Death Markov Process
• introduces an approximate analytical solution which can
be computed with no complexity and which is reversible
These techniques are applicable since the minimum interarrival of a request is greater than a server period. Unfortunately exists situations in which this assumption is not feasible. An important example is using resource reservation to scheduling interrupts. In order to consider also this situation, another important novel result of this thesis is:
• to introduce a new model for scheduling interrupts
In addition, some practical examples of using resource reservation are presented.
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Manica, Nicola. "Stochastic Analysis of a resource reservation system". Doctoral thesis, University of Trento, 2013. http://eprints-phd.biblio.unitn.it/1052/1/Manica-PhD-thesis-UniTn.pdf.
Pełny tekst źródłaStreszczenie:
An unmistakable trend in embedded systems is the growth of
soft real-time computing. A soft real-time application is one for which deadlines can occasionally be missed, but the probability of this event has to be controllable and predictable.
This work is aimed to close the gap in the research of stochastic real-time analysis related to resource reservation scheduling algorithms. This dissertation attempts to:
1. give a quick overview of classic real-time analysis
2. analyze the problems related to use the well-known techniques in the context of soft real-time applications:
• overvalue the assignation of parameters as in hard real-
time systems based on worst case execution times
• time and memory complexity using the known theoretical
stochastic analysis
3. propose solutions able to overcome the limitation showed in point 2
4. show some specific examples (theoretical and practical) in which resource reservation lead to advantages.
The novel contributions of this thesis are:
• a new bound to predict the probability of a deadline misses in a resource reservation systems
• a very efficient numeric solution for matrix generated with well-know abstraction models of reservation based on Quasi Birth Death Markov Process
• an analytical solution, with some conservative approximations, for the same models.
• a new model for specific applications, like interrupts.
• experiments using resource reservation in different contexts
The thesis is evolved following two different approaches:
1. the first based on the exact model of reservation, and the contributions is:
• define a new pessimistic bound, efficient in term of computation, able to overcome the problem of complete knowledge of the computation time. The solution is an approximation of the real solution of the model.
2. the second based on an approximation model in which the
novel contributions are:
• presents an exact and numeric efficient solution for the
model based on Quasi Birth and Death Markov Process
• introduces an approximate analytical solution which can
be computed with no complexity and which is reversible
These techniques are applicable since the minimum interarrival of a request is greater than a server period. Unfortunately exists situations in which this assumption is not feasible. An important example is using resource reservation to scheduling interrupts. In order to consider also this situation, another important novel result of this thesis is:
• to introduce a new model for scheduling interrupts
In addition, some practical examples of using resource reservation are presented.