Markov Chains and Stochastic Stability

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Cambridge University Press, Apr 2, 2009 - Mathematics - 594 pages
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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.
 

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Contents

Markov models
21
Transition probabilities
48
Pseudoatoms
96
Topology and continuity
123
The nonlinear state space model
146
Transience and recurrence
171
Harris and topological recurrence
199
The existence 0f 1r
229
Geometric ergodicity
362
Sample paths and limit theorems
421
Positivity
462
Generalized classification criteria
482
Epilogue to the second edition
510
A Mud maps
532
B Testing for stability
538
Some mathematical background
552

Drift and regularity
256
Invariance and tightness
288
Ergodicity
313
fErgodicity and fregularity
336

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About the author (2009)

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