Continuous Time Markov Processes

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Continuous Time Markov Chains

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Author : William J. Anderson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Continuous Time Markov Chains written by William J. Anderson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Continuous time parameter Markov chains have been useful for modeling various random phenomena occurring in queueing theory, genetics, demography, epidemiology, and competing populations. This is the first book about those aspects of the theory of continuous time Markov chains which are useful in applications to such areas. It studies continuous time Markov chains through the transition function and corresponding q-matrix, rather than sample paths. An extensive discussion of birth and death processes, including the Stieltjes moment problem, and the Karlin-McGregor method of solution of the birth and death processes and multidimensional population processes is included, and there is an extensive bibliography. Virtually all of this material is appearing in book form for the first time.

Continuous Time Markov Decision Processes

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Author : Xianping Guo
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-18

Continuous Time Markov Decision Processes written by Xianping Guo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-18 with Mathematics categories.

Continuous-time Markov decision processes (MDPs), also known as controlled Markov chains, are used for modeling decision-making problems that arise in operations research (for instance, inventory, manufacturing, and queueing systems), computer science, communications engineering, control of populations (such as fisheries and epidemics), and management science, among many other fields. This volume provides a unified, systematic, self-contained presentation of recent developments on the theory and applications of continuous-time MDPs. The MDPs in this volume include most of the cases that arise in applications, because they allow unbounded transition and reward/cost rates. Much of the material appears for the first time in book form.

Continuous Time Markov Chains And Applications

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Author : George G. Yin
language : en
Publisher: Springer
Release Date : 2012-12-06

Continuous Time Markov Chains And Applications written by George G. Yin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book is concerned with continuous-time Markov chains. It develops an integrated approach to singularly perturbed Markovian systems, and reveals interrelations of stochastic processes and singular perturbations. In recent years, Markovian formulations have been used routinely for nu merous real-world systems under uncertainties. Quite often, the underlying Markov chain is subject to rather frequent fluctuations and the correspond ing states are naturally divisible to a number of groups such that the chain fluctuates very rapidly among different states within a group, but jumps less frequently from one group to another. Various applications in engineer ing, economics, and biological and physical sciences have posed increasing demands on an in-depth study of such systems. A basic issue common to many different fields is the understanding of the distribution and the struc ture of the underlying uncertainty. Such needs become even more pressing when we deal with complex and/or large-scale Markovian models, whose closed-form solutions are usually very difficult to obtain. Markov chain, a well-known subject, has been studied by a host of re searchers for many years. While nonstationary cases have been treated in the literature, much emphasis has been on stationary Markov chains and their basic properties such as ergodicity, recurrence, and stability. In contrast, this book focuses on singularly perturbed nonstationary Markov chains and their asymptotic properties. Singular perturbation theory has a long history and is a powerful tool for a wide variety of applications.

Continuous Time Markov Processes

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Author : Thomas Milton Liggett
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Continuous Time Markov Processes written by Thomas Milton Liggett and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes, and applies this theory to various special examples.

Brownian Motion Martingales And Stochastic Calculus

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Author : Jean-François Le Gall
language : en
Publisher: Springer
Release Date : 2016-04-28

Brownian Motion Martingales And Stochastic Calculus written by Jean-François Le Gall and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-28 with Mathematics categories.

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.

Markov Processes Brownian Motion And Time Symmetry

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Author : Kai Lai Chung
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-07-15

Markov Processes Brownian Motion And Time Symmetry written by Kai Lai Chung and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-15 with Mathematics categories.

From the reviews of the First Edition: "This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester course given by the author at the ETH, Zürich, in the spring of 1970. The author's aim was to present some of the best features of Markov processes and, in particular, of Brownian motion with a minimum of prerequisites and technicalities. The reader who becomes acquainted with the volume cannot but agree with the reviewer that the author was very successful in accomplishing this goal...The volume is very useful for people who wish to learn Markov processes but it seems to the reviewer that it is also of great interest to specialists in this area who could derive much stimulus from it. One can be convinced that it will receive wide circulation." (Mathematical Reviews) This new edition contains 9 new chapters which include new exercises, references, and multiple corrections throughout the original text.

Markov Chains

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Author : Pierre Bremaud
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Markov Chains written by Pierre Bremaud and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

In this book, the author begins with the elementary theory of Markov chains and very progressively brings the reader to the more advanced topics. He gives a useful review of probability that makes the book self-contained, and provides an appendix with detailed proofs of all the prerequisites from calculus, algebra, and number theory. A number of carefully chosen problems of varying difficulty are proposed at the close of each chapter, and the mathematics are slowly and carefully developed, in order to make self-study easier. The author treats the classic topics of Markov chain theory, both in discrete time and continuous time, as well as the connected topics such as finite Gibbs fields, nonhomogeneous Markov chains, discrete- time regenerative processes, Monte Carlo simulation, simulated annealing, and queuing theory. The result is an up-to-date textbook on stochastic processes. Students and researchers in operations research and electrical engineering, as well as in physics and biology, will find it very accessible and relevant.

Markov Processes For Stochastic Modeling

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Author : Oliver Ibe
language : en
Publisher: Newnes
Release Date : 2013-05-22

Markov Processes For Stochastic Modeling written by Oliver Ibe and has been published by Newnes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-22 with Mathematics categories.

Markov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. Covering a wide range of areas of application of Markov processes, this second edition is revised to highlight the most important aspects as well as the most recent trends and applications of Markov processes. The author spent over 16 years in the industry before returning to academia, and he has applied many of the principles covered in this book in multiple research projects. Therefore, this is an applications-oriented book that also includes enough theory to provide a solid ground in the subject for the reader. - Presents both the theory and applications of the different aspects of Markov processes - Includes numerous solved examples as well as detailed diagrams that make it easier to understand the principle being presented - Discusses different applications of hidden Markov models, such as DNA sequence analysis and speech analysis.

Controlled Markov Processes And Viscosity Solutions

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Author : Wendell H. Fleming
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-04

Controlled Markov Processes And Viscosity Solutions written by Wendell H. Fleming and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-04 with Mathematics categories.

This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.

An Introduction To Markov Processes

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Author : Daniel W. Stroock
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-11-23

An Introduction To Markov Processes written by Daniel W. Stroock and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-23 with Mathematics categories.

Provides a more accessible introduction than other books on Markov processes by emphasizing the structure of the subject and avoiding sophisticated measure theory Leads the reader to a rigorous understanding of basic theory