Markov Chains and Stochastic Stability
Markov Chains and Stochastic Stability
Richard L. Tweedie, University of Minnesota
Peter W. Glynn
$93.99
USDMeyn 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
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
Product details
May 2009Adobe eBook Reader
9780511512711
0 pages
0kg
4 b/w illus.
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 Î
- 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.
