Markov Chains and Stochastic Stability

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Authors:

Sean P. Meyn ⁰,
Richard L. Tweedie 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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Richard L. Tweedie
1. Department of Statistics, Colorado State University, Fort Collins, USA
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Part of the book series: Communications and Control Engineering (CCE)

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Table of contents (19 chapters)

Front Matter

Pages i-xvi

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Communication and Regeneration
1. Front Matter
  
  Pages 1-1
  
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2. Heuristics
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 3-22
  
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3. Markov Models
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 23-53
  
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4. Transition Probabilities
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 54-79
  
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5. Irreducibility
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 80-99
  
  PDF
6. Pseudo-Atoms
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 100-125
  
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7. Topology and Continuity
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 126-148
  
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8. The Nonlinear State Space Model
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 149-169
  
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Stability Structures
1. Front Matter
  
  Pages 171-171
  
  PDF
2. Transience and Recurrence
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 173-199
  
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3. Harris and Topological Recurrence
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 200-228
  
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4. The Existence of π
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 229-254
  
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5. Drift and Regularity
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 255-284
  
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6. Invariance and Tightness
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 285-305
  
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Convergence
1. Front Matter
  
  Pages 307-307
  
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2. Ergodicity
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 309-329
  
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3. f-Ergodicity and f-Regularity
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 330-353
  
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4. Geometric Ergodicity
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 354-381
  
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5. V-Uniform Ergodicity
  
  Sean P. Meyn, Richard L. Tweedie
  
  Pages 382-409
  
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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.

Keywords

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

Bibliographic Information

Book Title: Markov Chains and Stochastic Stability
Authors: Sean P. Meyn, Richard L. Tweedie
Series Title: Communications and Control Engineering
DOI: https://doi.org/10.1007/978-1-4471-3267-7
Publisher: Springer London
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag London Limited 1993
Softcover ISBN: 978-1-4471-3269-1Published: 12 December 2012
eBook ISBN: 978-1-4471-3267-7Published: 06 December 2012
Series ISSN: 0178-5354
Series E-ISSN: 2197-7119
Edition Number: 1
Number of Pages: XVI, 550
Number of Illustrations: 10 b/w illustrations
Topics: Mathematical and Computational Engineering, Communications Engineering, Networks, Control, Robotics, Mechatronics

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Table of contents (19 chapters)

Front Matter

Communication and Regeneration

Front Matter

Stability Structures

Front Matter

Convergence

Front Matter

About this book

Keywords

Authors and Affiliations

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

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

Bibliographic Information

Publish with us

Buy it now

Buying options

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