# selected topics on continuous time controlled markov chains and markov games

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## Selected Topics On Continuous Time Controlled Markov Chains And Markov Games

**Author :**Tomás Prieto-Rumeau

**ISBN :**9781848168480

**Genre :**Mathematics

**File Size :**78. 25 MB

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This book concerns continuous-time controlled Markov chains and Markov games. The former, which are also known as continuous-time Markov decision processes, form a class of stochastic control problems in which a single decision-maker has a wish to optimize a given objective function. In contrast, there are two or more decision-makers (or players, or controllers) trying to optimize its own objective function in a Markov game. Both decision-making processes appear in a large number of applications in economics, operations research, engineering, and computer science among other areas. The main features of the control and game models studied in the book are the continuous time variable, the denumerable state space, and that the control (or action) sets are Borel spaces. Moreover, the transition and reward rates of the dynamical system may be unbounded. The authors are interested in some aspects of controlled Markov chains and Markov games such as characterizing the optimal reward functions, and determining optimal policies for each of the optimality criteria studied here. The main focus is on advanced optimality criteria (such as, bias, variance, sensitive discount, and Blackwell optimality), though they also deal with the basic optimality criteria (discounted and average reward). A particular emphasis is made on the application of the results presented in this book. One of the main concerns is to propose assumptions on the control and game models that are easily verifiable (and verified) in practice. Moreover, algorithmic and computational issues are also analyzed. In particular, the authors propose approximation results that allow precise numerical approximations of the solution to some problems of practical interest. Applications to population models and epidemic processes are also shown.

## Optimization Control And Applications Of Stochastic Systems

**Author :**Daniel Hernández-Hernández

**ISBN :**9780817683375

**Genre :**Science

**File Size :**72. 67 MB

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This volume provides a general overview of discrete- and continuous-time Markov control processes and stochastic games, along with a look at the range of applications of stochastic control and some of its recent theoretical developments. These topics include various aspects of dynamic programming, approximation algorithms, and infinite-dimensional linear programming. In all, the work comprises 18 carefully selected papers written by experts in their respective fields. Optimization, Control, and Applications of Stochastic Systems will be a valuable resource for all practitioners, researchers, and professionals in applied mathematics and operations research who work in the areas of stochastic control, mathematical finance, queueing theory, and inventory systems. It may also serve as a supplemental text for graduate courses in optimal control and dynamic games.

## New Trends In Stochastic Analysis And Related Topics

**Author :**Huaizhong Zhao

**ISBN :**9789814397094

**Genre :**Mathematics

**File Size :**26. 96 MB

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The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc. Contents:Stochastic Geometric Partial Differential Equations (Zdzisław Brzeźniak, Beniamin Goldys and Martin Ondreját)Rough Paths on Manifolds (Thomas Cass, Christian Litterer and Terry Lyons)Averaging, Homogenization and Slow Manifolds for Stochastic Partial Differential Equations (Jinqiao Duan, Anthony Roberts and Wei Wang)A Burgers-Zeldovich Model for the Formation of Planetesimals via Nelson's Stochastic Mechanics (Richard Durran, Andrew Neate, Aubrey Truman and Oleg Smolyanov)Two Problems Concerning Brownian Motion on a Complete Riemannian Manifold (Elton P Hsu)Sticky Shuffle Product Hopf Algebras and Their Stochastic Representations (Robin Hudson)Chain Rules for Lévy Flows and Kolmogorov Equations for Associated Jump-Diffusions (Hiroshi Kunita)The Stochastic Differential Equation Approach to Analysis on Path Space (Xue-Mei Li)Pathwise Properties of Random Quadratic Mapping (Peng Lian and Huaizhong Zhao)Invariant Manifolds for Infinite Dimensional Random Dynamical Systems (Kening Lu and Björn Schmalfuβ)Some Topics on Dirichlet Forms (Zhi-Ming Ma and Wei Sun)Hamilton-Jacobi Theory and the Stochastic Elementary Formula (Andrew Neate and Aubrey Truman) Readership: Graduate students and researchers in stochastic analysis. Keywords:Stochastic Analysis;Stochastic Partial Differential Equations;Random Dynamical Systems;Brownian Motion on Manifolds;Dirichlet Forms;Rough Path Theory;Levy Process;Hamilton Jacobi Theory;Path Space Analysis;Malliavin CalculusKey Features:Articles are written by world leading researchersContains comprehensive review articles by authors who made fundamental contributions to relevant topicsTopics are carefully selected to reflect subjects currently of great interests

## Markov Chains

**Author :**J. R. Norris

**ISBN :**0521633966

**Genre :**Mathematics

**File Size :**55. 6 MB

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In this rigorous account the author studies both discrete-time and continuous-time chains. A distinguishing feature is an introduction to more advanced topics such as martingales and potentials, in the established context of Markov chains. There are applications to simulation, economics, optimal control, genetics, queues and many other topics, and a careful selection of exercises and examples drawn both from theory and practice. This is an ideal text for seminars on random processes or for those that are more oriented towards applications, for advanced undergraduates or graduate students with some background in basic probability theory.

## An Introduction To Stochastic Processes With Applications To Biology

**Author :**Linda J. S. Allen

**ISBN :**0130352187

**Genre :**Mathematics

**File Size :**82. 43 MB

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Plenty of examples, diagrams, and figures take readers step-by-step through well-known classical biological models to ensure complete understanding of stochastic formulation. Probability, Markov Chains, discrete time branching processes, population genetics, and birth and death chains. For biologists and other professionals who want a comprehensive, easy-to-follow introduction to stochastic formulation as it pertains to biology.

## Advances In Dynamic Games And Applications

**Author :**Eitan Altmann

**ISBN :**9781461201557

**Genre :**Mathematics

**File Size :**76. 95 MB

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Game theory is a rich and active area of research of which this new volume of the Annals of the International Society of Dynamic Games is yet fresh evidence. Since the second half of the 20th century, the area of dynamic games has man aged to attract outstanding mathematicians, who found exciting open questions requiring tools from a wide variety of mathematical disciplines; economists, so cial and political scientists, who used game theory to model and study competition and cooperative behavior; and engineers, who used games in computer sciences, telecommunications, and other areas. The contents of this volume are primarily based on selected presentation made at the 8th International Symposium of Dynamic Games and Applications, held in Chateau Vaalsbroek, Maastricht, the Netherlands, July 5-8, 1998; this conference took place under the auspices of the International Society of Dynamic Games (ISDG), established in 1990. The conference has been cosponsored by the Control Systems Society of the IEEE, IFAC (International Federation of Automatic Con trol), INRIA (Institute National de Recherche en Informatique et Automatique), and the University of Maastricht. One ofthe activities of the ISDG is the publica tion of the Annals. Every paper that appears in this volume has passed through a stringent reviewing process, as is the case with publications for archival journals.

## Probability Markov Chains Queues And Simulation

**Author :**William J. Stewart

**ISBN :**9781400832811

**Genre :**Mathematics

**File Size :**32. 57 MB

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Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role. The textbook is relevant to a wide variety of fields, including computer science, engineering, operations research, statistics, and mathematics. The textbook looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational point of view. Topics include the Chapman-Kolmogorov equations; irreducibility; the potential, fundamental, and reachability matrices; random walk problems; reversibility; renewal processes; and the numerical computation of stationary and transient distributions. The M/M/1 queue and its extensions to more general birth-death processes are analyzed in detail, as are queues with phase-type arrival and service processes. The M/G/1 and G/M/1 queues are solved using embedded Markov chains; the busy period, residual service time, and priority scheduling are treated. Open and closed queueing networks are analyzed. The final part of the book addresses the mathematical basis of simulation. Each chapter of the textbook concludes with an extensive set of exercises. An instructor's solution manual, in which all exercises are completely worked out, is also available (to professors only). Numerous examples illuminate the mathematical theories Carefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approach Each chapter concludes with an extensive set of exercises Professors: A supplementary Solutions Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html