Download or read book Approximating Countable Markov Chains written by David Freedman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: A long time ago I started writing a book about Markov chains, Brownian motion, and diffusion. I soon had two hundred pages of manuscript and my publisher was enthusiastic. Some years and several drafts later, I had a thousand pages of manuscript, and my publisher was less enthusiastic. So we made it a trilogy: Markov Chains Brownian Motion and Diffusion Approximating Countable Markov Chains familiarly - MC, B & D, and ACM. I wrote the first two books for beginning graduate students with some knowledge of probability; if you can follow Sections 10.4 to 10.9 of Markov Chains, you're in. The first two books are quite independent of one another, and completely independent of this one, which is a monograph explaining one way to think about chains with instantaneous states. The results here are supposed to be new, except when there are specific disclaimers. It's written in the framework of Markov chains; we wanted to reprint in this volume the MC chapters needed for reference. but this proved impossible. Most of the proofs in the trilogy are new, and I tried hard to make them explicit. The old ones were often elegant, but I seldom saw what made them go. With my own, I can sometimes show you why things work. And, as I will argue in a minute, my demonstrations are easier technically. If I wrote them down well enough, you may come to agree.
Download or read book Approximation countable Markov chains written by David Freedman and published by . This book was released on 1972 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Markov Chains written by David Freedman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: A long time ago I started writing a book about Markov chains, Brownian motion, and diffusion. I soon had two hundred pages of manuscript and my publisher was enthusiastic. Some years and several drafts later, I had a thousand pages of manuscript, and my publisher was less enthusiastic. So we made it a trilogy: Markov Chains Brownian Motion and Diffusion Approximating Countable Markov Chains familiarly - MC, B & D, and ACM. I wrote the first two books for beginning graduate students with some knowledge of probability; if you can follow Sections 10.4 to 10.9 of Markov Chains you're in. The first two books are quite independent of one another, and completely independent of the third. This last book is a monograph which explains one way to think about chains with instantaneous states. The results in it are supposed to be new, except where there are specific disclaim ers; it's written in the framework of Markov Chains. Most of the proofs in the trilogy are new, and I tried hard to make them explicit. The old ones were often elegant, but I seldom saw what made them go. With my own, I can sometimes show you why things work. And, as I will VB1 PREFACE argue in a minute, my demonstrations are easier technically. If I wrote them down well enough, you may come to agree.
Download or read book Topics in the Constructive Theory of Countable Markov Chains written by G. Fayolle and published by Cambridge University Press. This book was released on 1995-05-18 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides methods of analysing Markov chains based on Lyapunov functions.
Download or read book Markov Chains written by D. Revuz and published by Elsevier. This book was released on 2008-07-15 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the revised and augmented edition of a now classic book which is an introduction to sub-Markovian kernels on general measurable spaces and their associated homogeneous Markov chains. The first part, an expository text on the foundations of the subject, is intended for post-graduate students. A study of potential theory, the basic classification of chains according to their asymptotic behaviour and the celebrated Chacon-Ornstein theorem are examined in detail. The second part of the book is at a more advanced level and includes a treatment of random walks on general locally compact abelian groups. Further chapters develop renewal theory, an introduction to Martin boundary and the study of chains recurrent in the Harris sense. Finally, the last chapter deals with the construction of chains starting from a kernel satisfying some kind of maximum principle.
Download or read book Handbook of Markov Decision Processes written by Eugene A. Feinberg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eugene A. Feinberg Adam Shwartz This volume deals with the theory of Markov Decision Processes (MDPs) and their applications. Each chapter was written by a leading expert in the re spective area. The papers cover major research areas and methodologies, and discuss open questions and future research directions. The papers can be read independently, with the basic notation and concepts ofSection 1.2. Most chap ters should be accessible by graduate or advanced undergraduate students in fields of operations research, electrical engineering, and computer science. 1.1 AN OVERVIEW OF MARKOV DECISION PROCESSES The theory of Markov Decision Processes-also known under several other names including sequential stochastic optimization, discrete-time stochastic control, and stochastic dynamic programming-studiessequential optimization ofdiscrete time stochastic systems. The basic object is a discrete-time stochas tic system whose transition mechanism can be controlled over time. Each control policy defines the stochastic process and values of objective functions associated with this process. The goal is to select a "good" control policy. In real life, decisions that humans and computers make on all levels usually have two types ofimpacts: (i) they cost orsavetime, money, or other resources, or they bring revenues, as well as (ii) they have an impact on the future, by influencing the dynamics. In many situations, decisions with the largest immediate profit may not be good in view offuture events. MDPs model this paradigm and provide results on the structure and existence of good policies and on methods for their calculation.
Download or read book Markov Chains written by J. R. Norris and published by Cambridge University Press. This book was released on 1998-07-28 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov chains are central to the understanding of random processes. This is not only because they pervade the applications of random processes, but also because one can calculate explicitly many quantities of interest. This textbook, aimed at advanced undergraduate or MSc students with some background in basic probability theory, focuses on Markov chains and quickly develops a coherent and rigorous theory whilst showing also how actually to apply it. Both discrete-time and continuous-time chains are studied. 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 exercises and examples drawn both from theory and practice. It will therefore be an ideal text either for elementary courses on random processes or those that are more oriented towards applications.
Download or read book Markov Chains written by Randal Douc and published by Springer. This book was released on 2018-12-11 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the classical theory of Markov chains on general state-spaces as well as many recent developments. The theoretical results are illustrated by simple examples, many of which are taken from Markov Chain Monte Carlo methods. The book is self-contained, while all the results are carefully and concisely proven. Bibliographical notes are added at the end of each chapter to provide an overview of the literature. Part I lays the foundations of the theory of Markov chain on general states-space. Part II covers the basic theory of irreducible Markov chains on general states-space, relying heavily on regeneration techniques. These two parts can serve as a text on general state-space applied Markov chain theory. Although the choice of topics is quite different from what is usually covered, where most of the emphasis is put on countable state space, a graduate student should be able to read almost all these developments without any mathematical background deeper than that needed to study countable state space (very little measure theory is required). Part III covers advanced topics on the theory of irreducible Markov chains. The emphasis is on geometric and subgeometric convergence rates and also on computable bounds. Some results appeared for a first time in a book and others are original. Part IV are selected topics on Markov chains, covering mostly hot recent developments.
Download or read book Markov Chains written by Kai Lai Chung and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: J. Neveu, 1962 in Zentralblatt fr Mathematik, 92. Band Heft 2, p. 343: "Ce livre crit par l'un des plus minents spcialistes en la matire, est un expos trs dtaill de la thorie des processus de Markov dfinis sur un espace dnombrable d'tats et homognes dans le temps (chaines stationnaires de Markov)." N. Jain, 2008 in Selected Works of Kai Lai Chung, edited by Farid AitSahlia (University of Florida, USA), Elton Hsu (Northwestern University, USA), & Ruth Williams (University of California-San Diego, USA), Chapter 1, p. 15: "This monograph deals with countable state Markov chains in both discrete time (Part I) and continuous time (Part II). ... Much of Kai Lai's fundamental work in the field is included in this monograph. Here, for the first time, Kai Lai gave a systematic exposition of the subject which includes classification of states, ratio ergodic theorems, and limit theorems for functionals of the chain."
Download or read book Brownian Motion and Diffusion written by David Freedman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: A long time ago I started writing a book about Markov chains, Brownian motion, and diffusion. I soon had two hundred pages of manuscript and my publisher was enthusiastic. Some years and several drafts later, I had a thot:sand pages of manuscript, and my publisher was less enthusiastic. So we made it a trilogy: Markov Chains Brownian Motion and Diffusion Approximating Countable Markov Chains familiarly - Me, B & D, and ACM. I wrote the first two books for beginning graduate students with some knowledge of probability; if you can follow Sections 3.4 to 3.9 of Brownian Motion and Diffusion you're in. The first two books are quite independent of one another, and completely independent of the third. This last book is a monograph, which explains one way to think about chains with instantaneous states. The results in it are supposed to be new, except where there are spe cific disclaimers; it's written in the framework of Markov Chains. Most of the proofs in the trilogy are new, and I tried hard to make them explicit. The old ones were often elegant, but I seldom saw what made them go. With my own, I can sometimes show you why things work. And, as I will argue in a minute, my demonstrations are easier technically. If I wrote them down well enough, you may come to agree.
Download or read book Essentials of Stochastic Processes written by Richard Durrett and published by Springer. This book was released on 2016-11-07 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved; for example, the difficult subject of martingales is delayed until its usefulness can be applied in the treatment of mathematical finance.
Download or read book Markov Chains and Stochastic Stability written by Sean P. Meyn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov Chains and Stochastic Stability is part of the Communications and Control Engineering Series (CCES) edited by Professors B.W. Dickinson, E.D. Sontag, M. Thoma, A. Fettweis, J.L. Massey and J.W. Modestino. The area of Markov chain theory and application has matured over the past 20 years into something more accessible and complete. It is of increasing interest and importance. This publication deals with the action of Markov chains on general state spaces. It discusses the theories and the use to be gained, concentrating on the areas of engineering, operations research and control theory. Throughout, the theme of stochastic stability and the search for practical methods of verifying such stability, provide a new and powerful technique. This does not only affect applications but also the development of the theory itself. The impact of the theory on specific models is discussed in detail, in order to provide examples as well as to demonstrate the importance of these models. Markov Chains and Stochastic Stability can be used as a textbook on applied Markov chain theory, provided that one concentrates on the main aspects only. It is also of benefit to graduate students with a standard background in countable space stochastic models. Finally, the book can serve as a research resource and active tool for practitioners.
Download or read book Discrete Time Markov Chains written by G. George Yin and published by Springer Science & Business Media. This book was released on 2005-10-04 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on two-time-scale Markov chains in discrete time. Our motivation stems from existing and emerging applications in optimization and control of complex systems in manufacturing, wireless communication, and ?nancial engineering. Much of our e?ort in this book is devoted to designing system models arising from various applications, analyzing them via analytic and probabilistic techniques, and developing feasible compu- tionalschemes. Ourmainconcernistoreducetheinherentsystemcompl- ity. Although each of the applications has its own distinct characteristics, all of them are closely related through the modeling of uncertainty due to jump or switching random processes. Oneofthesalientfeaturesofthisbookistheuseofmulti-timescalesin Markovprocessesandtheirapplications. Intuitively,notallpartsorcom- nents of a large-scale system evolve at the same rate. Some of them change rapidly and others vary slowly. The di?erent rates of variations allow us to reduce complexity via decomposition and aggregation. It would be ideal if we could divide a large system into its smallest irreducible subsystems completely separable from one another and treat each subsystem indep- dently. However, this is often infeasible in reality due to various physical constraints and other considerations. Thus, we have to deal with situations in which the systems are only nearly decomposable in the sense that there are weak links among the irreducible subsystems, which dictate the oc- sional regime changes of the system. An e?ective way to treat such near decomposability is time-scale separation. That is, we set up the systems as if there were two time scales, fast vs. slow. xii Preface Followingthetime-scaleseparation,weusesingularperturbationmeth- ology to treat the underlying systems.
Download or read book Martingales and Markov Chains written by Paolo Baldi and published by CRC Press. This book was released on 2002-04-26 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough grounding in Markov chains and martingales is essential in dealing with many problems in applied probability, and is a gateway to the more complex situations encountered in the study of stochastic processes. Exercises are a fundamental and valuable training tool that deepen students' understanding of theoretical principles and prepare them to tackle real problems. In addition to a quick but thorough exposition of the theory, Martingales and Markov Chains: Solved Exercises and Elements of Theory presents, more than 100 exercises related to martingales and Markov chains with a countable state space, each with a full and detailed solution. The authors begin with a review of the basic notions of conditional expectations and stochastic processes, then set the stage for each set of exercises by recalling the relevant elements of the theory. The exercises range in difficulty from the elementary, requiring use of the basic theory, to the more advanced, which challenge the reader's initiative. Each section also contains a set of problems that open the door to specific applications. Designed for senior undergraduate- and graduate level students, this text goes well beyond merely offering hints for solving the exercises, but it is much more than just a solutions manual. Within its solutions, it provides frequent references to the relevant theory, proposes alternative ways of approaching the problem, and discusses and compares the arguments involved.
Download or read book Markov Chains and Stochastic Stability written by Sean Meyn and published by Cambridge University Press. This book was released on 2009-04-02 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: New up-to-date edition of this influential classic on Markov chains in general state spaces. Proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background. New commentary by Sean Meyn, including updated references, reflects developments since 1996.
Download or read book Markov Chains and Invariant Probabilities written by Onésimo Hernández-Lerma and published by Birkhäuser. This book was released on 2012-12-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about discrete-time, time-homogeneous, Markov chains (Mes) and their ergodic behavior. To this end, most of the material is in fact about stable Mes, by which we mean Mes that admit an invariant probability measure. To state this more precisely and give an overview of the questions we shall be dealing with, we will first introduce some notation and terminology. Let (X,B) be a measurable space, and consider a X-valued Markov chain ~. = {~k' k = 0, 1, ... } with transition probability function (t.pJ.) P(x, B), i.e., P(x, B) := Prob (~k+1 E B I ~k = x) for each x E X, B E B, and k = 0,1, .... The Me ~. is said to be stable if there exists a probability measure (p.m.) /.l on B such that (*) VB EB. /.l(B) = Ix /.l(dx) P(x, B) If (*) holds then /.l is called an invariant p.m. for the Me ~. (or the t.p.f. P).
Download or read book Countable Markov Chains with an Application to Queueing Theory written by Ray Collins Owens and published by . This book was released on 1966 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
