Markov Chains and Stochastic Stability

Markov Chains and Stochastic Stability PDF Author: Sean P. Meyn
Publisher: Springer Science & Business Media
ISBN: 144713267X
Category : Technology & Engineering
Languages : en
Pages : 559

Book Description
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.

Markov Chains and Stochastic Stability

Markov Chains and Stochastic Stability PDF Author: Sean Meyn
Publisher: Cambridge University Press
ISBN: 1139477978
Category : Mathematics
Languages : en
Pages : 595

Book Description
Meyn and Tweedie is back! The bible on Markov chains in general state spaces has been brought up to date to reflect developments in the field since 1996 - many of them sparked by publication of the first edition. The pursuit of more efficient simulation algorithms for complex Markovian models, or algorithms for computation of optimal policies for controlled Markov models, has opened new directions for research on Markov chains. As a result, new applications have emerged across a wide range of topics including optimisation, statistics, and economics. New commentary and an epilogue by Sean Meyn summarise recent developments and references have been fully updated. This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.

Markov Chains and Stochastic Stability

Markov Chains and Stochastic Stability PDF Author: Sean Meyn
Publisher: Cambridge University Press
ISBN: 0521731828
Category : Mathematics
Languages : en
Pages : 623

Book Description
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.

Strong Stable Markov Chains

Strong Stable Markov Chains PDF Author: N. V. Kartashov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110917769
Category : Mathematics
Languages : en
Pages : 144

Book Description
No detailed description available for "Strong Stable Markov Chains".

General Irreducible Markov Chains and Non-Negative Operators

General Irreducible Markov Chains and Non-Negative Operators PDF Author: Esa Nummelin
Publisher: Cambridge University Press
ISBN: 9780521604949
Category : Mathematics
Languages : en
Pages : 176

Book Description
Presents the theory of general irreducible Markov chains and its connection to the Perron-Frobenius theory of nonnegative operators.

Ergodicity and Stability of Stochastic Processes

Ergodicity and Stability of Stochastic Processes PDF Author: A. A. Borovkov
Publisher: Wiley
ISBN: 9780471979135
Category : Mathematics
Languages : en
Pages : 0

Book Description
Translated from Russian, this book is an up-to-date account of ergodicity and of the stability of random processes. Important examples are Markov chains (MC) in arbitrary state space, stochastic recursive sequences (SRC) and MC in random environments (MCRI), as well as their continous time analogues.

Markov Chains with Stationary Transition Probabilities

Markov Chains with Stationary Transition Probabilities PDF Author: Kai Lai Chung
Publisher: Springer
ISBN: 3642496865
Category : Mathematics
Languages : en
Pages : 287

Book Description
The theory of Markov chains, although a special case of Markov processes, is here developed for its own sake and presented on its own merits. In general, the hypothesis of a denumerable state space, which is the defining hypothesis of what we call a "chain" here, generates more clear-cut questions and demands more precise and definitive an swers. For example, the principal limit theorem (§§ 1. 6, II. 10), still the object of research for general Markov processes, is here in its neat final form; and the strong Markov property (§ 11. 9) is here always applicable. While probability theory has advanced far enough that a degree of sophistication is needed even in the limited context of this book, it is still possible here to keep the proportion of definitions to theorems relatively low. . From the standpoint of the general theory of stochastic processes, a continuous parameter Markov chain appears to be the first essentially discontinuous process that has been studied in some detail. It is common that the sample functions of such a chain have discontinuities worse than jumps, and these baser discontinuities play a central role in the theory, of which the mystery remains to be completely unraveled. In this connection the basic concepts of separability and measurability, which are usually applied only at an early stage of the discussion to establish a certain smoothness of the sample functions, are here applied constantly as indispensable tools.

Continuous-Time Markov Chains and Applications

Continuous-Time Markov Chains and Applications PDF Author: George G. Yin
Publisher: Springer
ISBN: 1461206278
Category : Mathematics
Languages : en
Pages : 358

Book Description
Using a singular perturbation approach, this is a systematic treatment of those systems that naturally arise in queuing theory, control and optimisation, and manufacturing, gathering a number of ideas which were previously scattered throughout the literature. The book presents results on asymptotic expansions of the corresponding probability distributions, functional occupation measures, exponential upper bounds, and asymptotic normality. To bridge the gap between theory and applications, a large portion of the book is devoted to various applications, thus reducing the dimensionality for problems under Markovian disturbances and providing tools for dealing with large-scale and complex real-world situations. Much of this stems from the authors'recent research, presenting results which have not appeared elsewhere. An important reference for researchers in applied mathematics, probability and stochastic processes, operations research, control theory, and optimisation.
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