Probabilistic Methods in Markov Chains PDF Download
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Author: K. L. Chung
Publisher:
ISBN:
Category : Equations
Languages : en
Pages : 80
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Book Description
Author: K. L. Chung
Publisher:
ISBN:
Category : Equations
Languages : en
Pages : 80
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Book Description
Author: Donald Austin
Publisher:
ISBN:
Category : Equations
Languages : en
Pages : 32
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Book Description
We investigate analytic properties of non-negative matrices satisfying probabilistically motivated functional relations which are weaker than the semi-group condition. The fundamental differentiation theorem for transition functions of a Markov process is proved in the abstract space case.
Author: K. L. Chung
Publisher:
ISBN:
Category : Equations
Languages : en
Pages : 34
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Book Description
Author: J. R. Norris
Publisher: Cambridge University Press
ISBN: 9780521633963
Category : Mathematics
Languages : en
Pages : 260
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Book Description
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.
Author: William J. Stewart
Publisher: Princeton University Press
ISBN: 1400832810
Category : Mathematics
Languages : en
Pages : 777
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Book Description
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
Author: Eugene A. Feinberg
Publisher: Springer Science & Business Media
ISBN: 1461508053
Category : Business & Economics
Languages : en
Pages : 560
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Book Description
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.
Author: Pierre Brémaud
Publisher: Springer
ISBN: 3319434764
Category : Mathematics
Languages : en
Pages : 561
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Book Description
The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory. The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book.
Author: R. Syski
Publisher: IOS Press
ISBN: 9789051990607
Category : Computers
Languages : en
Pages : 564
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Book Description
This book is a survey of work on passage times in stable Markov chains with a discrete state space and a continuous time. Passage times have been investigated since early days of probability theory and its applications. The best known example is the first entrance time to a set, which embraces waiting times, busy periods, absorption problems, extinction phenomena, etc. Another example of great interest is the last exit time from a set. The book presents a unifying treatment of passage times, written in a systematic manner and based on modern developments. The appropriate unifying framework is provided by probabilistic potential theory, and the results presented in the text are interpreted from this point of view. In particular, the crucial role of the Dirichlet problem and the Poisson equation is stressed. The work is addressed to applied probalilists, and to those who are interested in applications of probabilistic methods in their own areas of interest. The level of presentation is that of a graduate text in applied stochastic processes. Hence, clarity of presentation takes precedence over secondary mathematical details whenever no serious harm may be expected. Advanced concepts described in the text gain nowadays growing acceptance in applied fields, and it is hoped that this work will serve as an useful introduction. Abstracted by Mathematical Reviews, issue 94c
Author: Olle Häggström
Publisher: Cambridge University Press
ISBN: 9780521890014
Category : Mathematics
Languages : en
Pages : 132
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Book Description
Based on a lecture course given at Chalmers University of Technology, this 2002 book is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before applying it to study a range of randomized algorithms with important applications in optimization and other problems in computing. Amongst the algorithms covered are the Markov chain Monte Carlo method, simulated annealing, and the recent Propp-Wilson algorithm. This book will appeal not only to mathematicians, but also to students of statistics and computer science. The subject matter is introduced in a clear and concise fashion and the numerous exercises included will help students to deepen their understanding.
Author: David Asher Levin
Publisher: Amer Mathematical Society
ISBN: 9780821847398
Category : Mathematics
Languages : en
Pages : 371
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Book Description
This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of random walks on networks, including hitting and cover times, and analyses of several methods of shuffling cards. As a prerequisite, the authors assume a modest understanding of probability theory and linear algebra at an undergraduate level. ""Markov Chains and Mixing Times"" is meant to bring the excitement of this active area of research to a wide audience.
