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Markov Chains and Stochastic Stability

2nd Edition

$68.00 USD

Part of Cambridge Mathematical Library

  • Date Published: May 2009
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511512711

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About the Authors
  • 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.

    • The modern classic, available in print for the first time in 10 years
    • The 1994 ORSA/TIMS Best Publication on Applied Probability Award winner, brought up to date to reflect recent developments
    • Now includes a prologue by Peter W. Glynn
    Read more

    Reviews & endorsements

    'This second edition remains true to the remarkable standards of scholarship established by the first edition … it will no doubt be a very welcome addition to the literature.' Peter W. Glynn, Prologue to the Second Edition

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    Product details

    • Edition: 2nd Edition
    • Date Published: May 2009
    • format: Adobe eBook Reader
    • isbn: 9780511512711
    • contains: 4 b/w illus.
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    List of figures
    Prologue to the second edition Peter W. Glynn
    Preface to the second edition Sean Meyn
    Preface to the first edition
    Part I. Communication and Regeneration:
    1. Heuristics
    2. Markov models
    3. Transition probabilities
    4. Irreducibility
    5. Pseudo-atoms
    6. Topology and continuity
    7. The nonlinear state space model
    Part II. Stability Structures:
    8. Transience and recurrence
    9. Harris and topological recurrence
    10. The existence of Π
    11. Drift and regularity
    12. Invariance and tightness
    Part III. Convergence:
    13. Ergodicity
    14. f-Ergodicity and f-regularity
    15. Geometric ergodicity
    16. V-Uniform ergodicity
    17. Sample paths and limit theorems
    18. Positivity
    19. Generalized classification criteria
    20. Epilogue to the second edition
    Part IV. Appendices: A. Mud maps
    B. Testing for stability
    C. Glossary of model assumptions
    D. Some mathematical background
    Bibliography
    Indexes.

  • Authors

    Sean Meyn, University of Illinois, Urbana-Champaign
    Sean Meyn is a professor in the Department of Electrical and Computer Engineering and director of the Division and Control Laboratory of the Coordinated Science Laboratory at the University of Illinois. He has served on the editorial boards of several journals in areas of systems and control and applied probability.

    Richard L. Tweedie, University of Minnesota
    Richard L. Tweedie was Professor and Head of the Division of Biostatistics at the University of Minnesota before his death in 2001.

    Prologue by

    Peter W. Glynn

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