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Dissertations / Theses on the topic 'Stochastic differential equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Bahar, Arifah. "Applications of stochastic differential equations and stochastic delay differential equations in population dynamics." Thesis, University of Strathclyde, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.415294.

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2

Dareiotis, Anastasios Constantinos. "Stochastic partial differential and integro-differential equations." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/14186.

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In this work we present some new results concerning stochastic partial differential and integro-differential equations (SPDEs and SPIDEs) that appear in non-linear filtering. We prove existence and uniqueness of solutions of SPIDEs, we give a comparison principle and we suggest an approximation scheme for the non-local integral operators. Regarding SPDEs, we use techniques motivated by the work of De Giorgi, Nash, and Moser, in order to derive global and local supremum estimates, and a weak Harnack inequality.

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3

Abourashchi, Niloufar. "Stability of stochastic differential equations." Thesis, University of Leeds, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.509828.

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4

Zhang, Qi. "Stationary solutions of stochastic partial differential equations and infinite horizon backward doubly stochastic differential equations." Thesis, Loughborough University, 2008. https://dspace.lboro.ac.uk/2134/34040.

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In this thesis we study the existence of stationary solutions for stochastic partial differential equations. We establish a new connection between solutions of backward doubly stochastic differential equations (BDSDEs) on infinite horizon and the stationary solutions of the SPDEs. For this, we prove the existence and uniqueness of the L2ρ (Rd; R1) × L2ρ (Rd; Rd) valued solutions of BDSDEs with Lipschitz nonlinear term on both finite and infinite horizons, so obtain the solutions of initial value problems and the stationary weak solutions (independent of any initial value) of SPDEs. Also the L2

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5

Hollingsworth, Blane Jackson Schmidt Paul G. "Stochastic differential equations a dynamical systems approach /." Auburn, Ala, 2008. http://repo.lib.auburn.edu/EtdRoot/2008/SPRING/Mathematics_and_Statistics/Dissertation/Hollingsworth_Blane_43.pdf.

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6

Mu, Tingshu. "Backward stochastic differential equations and applications : optimal switching, stochastic games, partial differential equations and mean-field." Thesis, Le Mans, 2020. http://www.theses.fr/2020LEMA1023.

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Cette thèse est relative aux Equations Différentielles Stochastique Rétrogrades (EDSRs) réfléchies avec deux obstacles et leurs applications aux jeux de switching de somme nulle, aux systèmes d’équations aux dérivées partielles, aux problèmes de mean-field. Il y a deux parties dans cette thèse. La première partie porte sur le switching optimal stochastique et est composée de deux travaux. Dans le premier travail, nous montrons l’existence de la solution d’un système d’EDSR réfléchies à obstacles bilatéraux interconnectés dans le cadre probabiliste général. Ce problème est lié à un jeu de switc

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7

Rassias, Stamatiki. "Stochastic functional differential equations and applications." Thesis, University of Strathclyde, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486536.

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The general truth that the principle of causality, that is, the future state of a system is independent of its past history, cannot support all the cases under consideration, leads to the introduction of the FDEs. However, the strong need of modelling real life problems, demands the inclusion of stochasticity. Thus, the appearance of the SFDEs (special case of which is the SDDEs) is necessary and definitely unavoidable. It has been almost a century since Langevin's model that the researchers incorporate noise terms into their work. Two of the main research interests are linked with the existen

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8

Hofmanová, Martina. "Degenerate parabolic stochastic partial differential equations." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2013. http://tel.archives-ouvertes.fr/tel-00916580.

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In this thesis, we address several problems arising in the study of nondegenerate and degenerate parabolic SPDEs, stochastic hyperbolic conservation laws and SDEs with continues coefficients. In the first part, we are interested in degenerate parabolic SPDEs, adapt the notion of kinetic formulation and kinetic solution and establish existence, uniqueness as well as continuous dependence on initial data. As a preliminary result we obtain regularity of solutions in the nondegenerate case under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives. In the s

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9

Curry, Charles. "Algebraic structures in stochastic differential equations." Thesis, Heriot-Watt University, 2014. http://hdl.handle.net/10399/2791.

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We define a new numerical integration scheme for stochastic differential equations driven by Levy processes with uniformly lower mean square remainder than that of the scheme of the same strong order of convergence obtained by truncating the stochastic Taylor series. In doing so we generalize recent results concerning stochastic differential equations driven by Wiener processes. The aforementioned works studied integration schemes obtained by applying an invertible mapping to the stochastic Taylor series, truncating the resulting series and applying the inverse of the original mapping. The shu

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10

Rajotte, Matthew. "Stochastic Differential Equations and Numerical Applications." VCU Scholars Compass, 2014. http://scholarscompass.vcu.edu/etd/3383.

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We will explore the topic of stochastic differential equations (SDEs) first by developing a foundation in probability theory and It\^o calculus. Formulas are then derived to simulate these equations analytically as well as numerically. These formulas are then applied to a basic population model as well as a logistic model and the various methods are compared. Finally, we will study a model for low dose anthrax exposure which currently implements a stochastic probabilistic uptake in a deterministic differential equation, and analyze how replacing the probablistic uptake with an SDE alters the d

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11

Nie, Tianyang. "Stochastic differential equations with constraints on the state : backward stochastic differential equations, variational inequalities and fractional viability." Thesis, Brest, 2012. http://www.theses.fr/2012BRES0047.

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Le travail de thèse est composé de trois thèmes principaux : le premier étudie l'existence et l'unicité pour des équations différentielles stochastiques (EDS) progressives-rétrogrades fortement couplées avec des opérateurs sous-différentiels dans les deux équations, dans l’équation progressive ainsi que l’équation rétrograde, et il discute également un nouveau type des inégalités variationnelles partielles paraboliques associées, avec deux opérateurs sous-différentiels, l’un agissant sur le domaine de l’état, l’autre sur le co-domaine. Le second thème est celui des EDS rétrogrades sans ainsi q

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12

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 measur

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13

Reiss, Markus. "Nonparametric estimation for stochastic delay differential equations." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964782480.

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14

Yalman, Hatice. "Change Point Estimation for Stochastic Differential Equations." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-5748.

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<p>A stochastic differential equationdriven by a Brownian motion where the dispersion is determined by a parameter is considered. The parameter undergoes a change at a certain time point. Estimates of the time change point and the parameter, before and after that time, is considered.The estimates were presented in Lacus 2008. Two cases are considered: (1) the drift is known, (2) the drift is unknown and the dispersion space-independent. Applications to Dow-Jones index 1971-1974 and Goldmann-Sachs closings 2005-- May 2009 are given.</p>

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15

Leng, Weng San. "Backward stochastic differential equations and option pricing." Thesis, University of Macau, 2003. http://umaclib3.umac.mo/record=b1447308.

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16

Tunc, Vildan. "Two Studies On Backward Stochastic Differential Equations." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614541/index.pdf.

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Backward stochastic differential equations appear in many areas of research including mathematical finance, nonlinear partial differential equations, financial economics and stochastic control. The first existence and uniqueness result for nonlinear backward stochastic differential equations was given by Pardoux and Peng (Adapted solution of a backward stochastic differential equation. System and Control Letters, 1990). They looked for an adapted pair of processes {x(t)<br>y(t)}<br>t is in [0<br>1]} with values in Rd and Rd&times<br>k respectively, which solves an equation of the form: x(t) +

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17

Zettervall, Niklas. "Multi-scale methods for stochastic differential equations." Thesis, Umeå universitet, Institutionen för fysik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-53704.

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Standard Monte Carlo methods are used extensively to solve stochastic differential equations. This thesis investigates a Monte Carlo (MC) method called multilevel Monte Carlo that solves the equations on several grids, each with a specific number of grid points. The multilevel MC reduces the computational cost compared to standard MC. When using a fixed computational cost the variance can be reduced by using the multilevel method compared to the standard one. Discretization and statistical error calculations are also being conducted and the possibility to evaluate the errors coupled with the m

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18

Matetski, Kanstantsin. "Discretisations of rough stochastic partial differential equations." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/81460/.

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This thesis consists of two parts, in both of which we consider approximations of rough stochastic PDEs and investigate convergence properties of the approximate solutions. In the first part we use the theory of (controlled) rough paths to define a solution for one-dimensional stochastic PDEs of Burgers type driven by an additive space-time white noise. We prove that natural numerical approximations of these equations converge to the solution of a corrected continuous equation and that their optimal convergence rate in the uniform topology (in probability) is arbitrarily close to 1/2 . In the

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19

Hashemi, Seyed Naser. "Singular perturbations in coupled stochastic differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ65244.pdf.

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20

Matsikis, Iakovos. "High gain control of stochastic differential equations." Thesis, University of Exeter, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.403248.

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21

Althubiti, Saeed. "STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE MEMORY." OpenSIUC, 2018. https://opensiuc.lib.siu.edu/dissertations/1544.

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In this dissertation, we discuss the existence and uniqueness of Ito-type stochastic functional differential equations with infinite memory using fixed point theorem technique. We also address the properties of the solution which are an upper bound for the pth moments of the solution and the Lp-regularity. Then, we provide an analysis to show the local asymptotic L2-stability of the trivial solution using fixed point theorem technique, and we give an approximation of the solution using Euler-Maruyama method providing the global error followed by simulating examples.

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22

Spantini, Alessio. "Preconditioning techniques for stochastic partial differential equations." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/82507.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2013.<br>This thesis was scanned as part of an electronic thesis pilot project.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 149-155).<br>This thesis is about preconditioning techniques for time dependent stochastic Partial Differential Equations arising in the broader context of Uncertainty Quantification. State-of-the-art methods for an efficient integration of stochastic PDEs require the solution field to lie on a low dimensional linear manifold. In cases when

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23

Kolli, Praveen C. "Topics in Rank-Based Stochastic Differential Equations." Research Showcase @ CMU, 2018. http://repository.cmu.edu/dissertations/1205.

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In this thesis, we tackle two problems. In the first problem, we study fluctuations of a system of diffusions interacting through the ranks when the number of diffusions goes to infinity. It is known that the empirical cumulative distribution function of such diffusions converges to a non-random limiting cumulative distribution function which satisfies the porous medium PDE. We show that the fluctuations of the empirical cumulative distribution function around its limit are governed by a suitable SPDE. In the second problem, we introduce common noise that has a rank preserving structure into s

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24

Prerapa, Surya Mohan. "Projection schemes for stochastic partial differential equations." Thesis, University of Southampton, 2009. https://eprints.soton.ac.uk/342800/.

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The focus of the present work is to develop stochastic reduced basis methods (SRBMs) for solving partial differential equations (PDEs) defined on random domains and nonlinear stochastic PDEs (SPDEs). SRBMs have been extended in the following directions: Firstly, an h-refinement strategy referred to as Multi-Element-SRBMs (ME-SRBMs) is developed for local refinement of the solution process. The random space is decomposed into subdomains where SRBMs are employed in each subdomain resulting in local response statistics. These local statistics are subsequently assimilated to compute the global sta

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25

Liu, Ge. "Statistical Inference for Multivariate Stochastic Differential Equations." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1562966204796479.

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26

Gauthier, Genevieve Carleton University Dissertation Mathematics and Statistics. "Multilevel bilinear system of stochastic differential equations." Ottawa, 1995.

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27

Zhang, Xiling. "On numerical approximations for stochastic differential equations." Thesis, University of Edinburgh, 2017. http://hdl.handle.net/1842/28931.

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This thesis consists of several problems concerning numerical approximations for stochastic differential equations, and is divided into three parts. The first one is on the integrability and asymptotic stability with respect to a certain class of Lyapunov functions, and the preservation of the comparison theorem for the explicit numerical schemes. In general, those properties of the original equation can be lost after discretisation, but it will be shown that by some suitable modification of the Euler scheme they can be preserved to some extent while keeping the strong convergence rate maintai

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28

Reiß, Markus. "Nonparametric estimation for stochastic delay differential equations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2002. http://dx.doi.org/10.18452/14741.

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Sei (X(t), t>= -r) ein stationärer stochastischer Prozess, der die affine stochastische Differentialgleichung mit Gedächtnis dX(t)=L(X(t+s))dt+sigma dW(t), t>= 0, löst, wobei sigma>0, (W(t), t>=0) eine Standard-Brownsche Bewegung und L ein stetiges lineares Funktional auf dem Raum der stetigen Funktionen auf [-r,0], dargestellt durch ein endliches signiertes Maß a, bezeichnet. Wir nehmen an, dass eine Trajektorie (X(t), -r 0, konvergiert. Diese Rate ist schlechter als in vielen klassischen Fällen. Wir beweisen jedoch eine untere Schranke, die zeigt, dass keine Schätzung eine bessere Rate im Mi

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29

Nguyen, Cu Ngoc. "Stochastic differential equations with long-memory input." Thesis, Queensland University of Technology, 2001.

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30

Sipiläinen, Eeva-Maria. "Pathwise view on solutions of stochastic differential equations." Thesis, University of Edinburgh, 1993. http://hdl.handle.net/1842/8202.

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The Ito-Stratonovich theory of stochastic integration and stochastic differential equations has several shortcomings, especially when it comes to existence and consistency with the theory of Lebesque-Stieltjes integration and ordinary differential equations. An attempt is made firstly, to isolate the path property, possessed by almost all Brownian paths, that makes the stochastic theory of integration work. Secondly, to construct a new concept of solutions for differential equations, which would have the required consistency and continuity properties, within a class of deterministic noise func

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31

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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32

Ahlip, Rehez Ajmal. "Stability & filtering of stochastic systems." Thesis, Queensland University of Technology, 1997.

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33

Banerjee, Paromita. "Numerical Methods for Stochastic Differential Equations and Postintervention in Structural Equation Models." Case Western Reserve University School of Graduate Studies / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1597879378514956.

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34

Moon, Kyoung-Sook. "Adaptive Algorithms for Deterministic and Stochastic Differential Equations." Doctoral thesis, KTH, Numerical Analysis and Computer Science, NADA, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3586.

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35

Guillouzic, Steve. "Fokker-Planck approach to stochastic delay differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ58279.pdf.

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36

Zerihun, Tadesse G. "Nonlinear Techniques for Stochastic Systems of Differential Equations." Scholar Commons, 2013. http://scholarcommons.usf.edu/etd/4970.

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Two of the most well-known nonlinear methods for investigating nonlinear dynamic processes in sciences and engineering are nonlinear variation of constants parameters and comparison method. Knowing the existence of solution process, these methods provide a very powerful tools for investigating variety of problems, for example, qualitative and quantitative properties of solutions, finding error estimates between solution processes of stochastic system and the corresponding nominal system, and inputs for the designing engineering and industrial problems. The aim of this work is to systematical

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37

Pilipenko, Andrey. "An introduction to stochastic differential equations with reflection." Universität Potsdam, 2014. http://opus.kobv.de/ubp/volltexte/2014/7078/.

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These lecture notes are intended as a short introduction to diffusion processes on a domain with a reflecting boundary for graduate students, researchers in stochastic analysis and interested readers. Specific results on stochastic differential equations with reflecting boundaries such as existence and uniqueness, continuity and Markov properties, relation to partial differential equations and submartingale problems are given. An extensive list of references to current literature is included. This book has its origins in a mini-course the author gave at the University of Potsdam and at the Tec

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38

Pokern, Yvo. "Fitting stochastic differential equations to molecular dynamics data." Thesis, University of Warwick, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.439586.

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39

Li, Qiming. "N-dimension numerical solution of stochastic differential equations." Thesis, University of Edinburgh, 2007. http://hdl.handle.net/1842/12417.

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We introduce an order γ(γ>1/2) strong scheme and an improved weak scheme for the numerical approximation of solutions to stochastic differential equations (SDEs), driven by N Weinner processes. The strong scheme, called the ¾ Scheme, which is dependent on a differently constructed Brownian path, involves the area terms to bring better asymptotic accuracy than any numerical method based on classic constructed N-Dimension Brownian path. We demonstrate how to construct such a Brownian path, besides how to subdivide the Brownian path to get a sequence of approximations which converges pathwise

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40

Luo, Ye. "Random periodic solutions of stochastic functional differential equations." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/16112.

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In this thesis, we study the existence of random periodic solutions for both nonlinear dissipative stochastic functional differential equations (SFDEs) and semilinear nondissipative SFDEs in C([-r,0],R^d). Under some sufficient conditions for the existence of global semiflows for SFDEs, by using pullback-convergence technique to SFDE, we obtain a general theorem about the existence of random periodic solutions. By applying coupled forward-backward infinite horizon integral equations method, we perform the argument of the relative compactness of Wiener-Sobolev spaces in C([0,τ],C([-r,0]L²(Ω)))

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41

Wang, Xince. "Quasilinear PDEs and forward-backward stochastic differential equations." Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/17383.

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In this thesis, first we study the unique classical solution of quasi-linear second order parabolic partial differential equations (PDEs). For this, we study the existence and uniqueness of the $L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{d}) \otimes L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{k})\otimes L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{k\times d})$ valued solution of forward backward stochastic differential equations (FBSDEs) with finite horizon, the regularity property of the solution of FBSDEs and the connection between the solution of FBSDEs and the solution of quasi-linear parabolic PDEs.

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42

Zhou, Yiqian. "Stability of stochastic differential equations in infinite dimensions." Thesis, University of Liverpool, 2012. http://livrepository.liverpool.ac.uk/10513/.

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In engineering, physics and economics, many dynamical systems involving with stochastic components and random noise are often modeled by stochastic models. The stochastic effects of these models are often used to describe the uncertainty about the operating systems. Motivated by the development of analysis and theory of stochastic processes, as well as the studies of natural sciences, the theory of stochastic differential equations in infinite dimensional spaces evolves gradually into a branch of modern analysis. Many qualitative properties of such systems have been studied in the past few dec

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43

Xiong, Sheng. "Stochastic Differential Equations: Some Risk and Insurance Applications." Diss., Temple University Libraries, 2011. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/133166.

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Mathematics<br>Ph.D.<br>In this dissertation, we have studied diffusion models and their applications in risk theory and insurance. Let Xt be a d-dimensional diffusion process satisfying a system of Stochastic Differential Equations defined on an open set G Rd, and let Ut be a utility function of Xt with U0 = u0. Let T be the first time that Ut reaches a level u^*. We study the Laplace transform of the distribution of T, as well as the probability of ruin, psileft(u_{0}right)=Prleft{ T<inftyright} , and other important probabilities. A class of exponential martingales is constructed to analyz

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44

Schmid, Matthias J. A. "A New Control Paradigm for Stochastic Differential Equations." Thesis, State University of New York at Buffalo, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10285670.

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<p> This study presents a novel comprehensive approach to the control of dynamic systems under uncertainty governed by stochastic differential equations (SDEs). Large Deviations (LD) techniques are employed to arrive at a control law for a large class of nonlinear systems minimizing sample path deviations. Thereby, a paradigm shift is suggested from point-in-time to sample path statistics on function spaces. </p><p> A suitable formal control framework which leverages embedded Freidlin-Wentzell theory is proposed and described in detail. This includes the precise definition of the control obj

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45

Kasonga, Raphael Abel Carleton University Dissertation Mathematics. "Asymptotic parameter estimation theory for stochastic differential equations." Ottawa, 1986.

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46

Jeisman, Joseph Ian. "Estimation of the parameters of stochastic differential equations." Thesis, Queensland University of Technology, 2006. https://eprints.qut.edu.au/16205/1/Joseph_Jesiman_Thesis.pdf.

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Stochastic di®erential equations (SDEs) are　central to much of modern finance theory and have been widely used to model the behaviour of key variables such as the　instantaneous short-term interest rate, asset prices, asset returns and their volatility.　The explanatory and/or predictive power of these models depends crucially on the particularisation of the model SDE(s) to real data through the choice of values for their parameters. In econometrics, optimal parameter estimates are generally considered to　be those that maximise the likelihood of the sample. In the context of the estimation of

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47

Jeisman, Joseph Ian. "Estimation of the parameters of stochastic differential equations." Queensland University of Technology, 2006. http://eprints.qut.edu.au/16205/.

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Stochastic di®erential equations (SDEs) are　central to much of modern finance theory and have been widely used to model the behaviour of key variables such as the　instantaneous short-term interest rate, asset prices, asset returns and their volatility.　The explanatory and/or predictive power of these models depends crucially on the particularisation of the model SDE(s) to real data through the choice of values for their parameters. In econometrics, optimal parameter estimates are generally considered to　be those that maximise the likelihood of the sample. In the context of the estimation of t

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48

Xu, Lina. "Simulation methods for stochastic differential equations in finance." Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/134388/1/Lina_Xu_Thesis.pdf.

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This thesis resolves a number of econometric problems relating to the use of stochastic differential equations based on computer-intensive simulation methods. Stochastic differential equations play an important role in modern finance. They have been used to model the trajectories of key variables such as short-term interest rates and the volatility of financial assets. The central theme of the thesis is the use of Hermite polynomials to approximate the transitional probability distribution functions of stochastic differential equations. Based on these approximations, a new method is proposed f

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49

Lythe, Grant David. "Stochastic slow-fast dynamics." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338108.

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50

Li, Wuchen. "A study of stochastic differential equations and Fokker-Planck equations with applications." Diss., Georgia Institute of Technology, 2016. http://hdl.handle.net/1853/54999.

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Fokker-Planck equations, along with stochastic differential equations, play vital roles in physics, population modeling, game theory and optimization (finite or infinite dimensional). In this thesis, we study three topics, both theoretically and computationally, centered around them. In part one, we consider the optimal transport for finite discrete states, which are on a finite but arbitrary graph. By defining a discrete 2-Wasserstein metric, we derive Fokker-Planck equations on finite graphs as gradient flows of free energies. By using dynamical viewpoint, we obtain an exponential convergenc

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