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Markov Chains and Stochastic Stability

  • Book
  • © 1993

Overview

Authors:
  1. Sean P. Meyn

    1. Coordinated Science Laboratory and the Department of Electrical and Computer Engineering, University of Illinois, Urbana, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Richard L. Tweedie

    1. Department of Statistics, Colorado State University, Fort Collins, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Communications and Control Engineering (CCE)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Communication and Regeneration

    1. Front Matter

      Pages 1-1
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    2. Heuristics

      • Sean P. Meyn, Richard L. Tweedie
      Pages 3-22

    3. Markov Models

      • Sean P. Meyn, Richard L. Tweedie
      Pages 23-53

    4. Transition Probabilities

      • Sean P. Meyn, Richard L. Tweedie
      Pages 54-79

    5. Irreducibility

      • Sean P. Meyn, Richard L. Tweedie
      Pages 80-99

    6. Pseudo-Atoms

      • Sean P. Meyn, Richard L. Tweedie
      Pages 100-125

    7. Topology and Continuity

      • Sean P. Meyn, Richard L. Tweedie
      Pages 126-148

    8. The Nonlinear State Space Model

      • Sean P. Meyn, Richard L. Tweedie
      Pages 149-169

  3. Stability Structures

    1. Front Matter

      Pages 171-171
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    2. Transience and Recurrence

      • Sean P. Meyn, Richard L. Tweedie
      Pages 173-199

    3. Harris and Topological Recurrence

      • Sean P. Meyn, Richard L. Tweedie
      Pages 200-228

    4. The Existence of π

      • Sean P. Meyn, Richard L. Tweedie
      Pages 229-254

    5. Drift and Regularity

      • Sean P. Meyn, Richard L. Tweedie
      Pages 255-284

    6. Invariance and Tightness

      • Sean P. Meyn, Richard L. Tweedie
      Pages 285-305

  4. Convergence

    1. Front Matter

      Pages 307-307
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    2. Ergodicity

      • Sean P. Meyn, Richard L. Tweedie
      Pages 309-329

    3. f-Ergodicity and f-Regularity

      • Sean P. Meyn, Richard L. Tweedie
      Pages 330-353

    4. Geometric Ergodicity

      • Sean P. Meyn, Richard L. Tweedie
      Pages 354-381

    5. V-Uniform Ergodicity

      • Sean P. Meyn, Richard L. Tweedie
      Pages 382-409
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Keywords

About this book

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.

Authors and Affiliations

  • Coordinated Science Laboratory and the Department of Electrical and Computer Engineering, University of Illinois, Urbana, USA

    Sean P. Meyn

  • Department of Statistics, Colorado State University, Fort Collins, USA

    Richard L. Tweedie

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