Markov Chains and Stochastic StabilityCambridge University Press, 02.04.2009 - 594 Seiten 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. |
Inhalt
Markov models | 21 |
Transition probabilities | 48 |
Irreducibility | 75 |
Pseudoatoms | 96 |
Topology and continuity | 123 |
The nonlinear state space model | 146 |
Transience and recurrence | 171 |
Harris and topological recurrence | 199 |
fErgodicity and fregularity | 336 |
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 |
The existence of π | 229 |
Drift and regularity | 256 |
Invariance and tightness | 288 |
Ergodicity | 313 |
Some mathematical background | 552 |
| 567 | |
| 587 | |
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4-irreducible absorbing set assumption atom bounded in probability Chapter CM(F compact set consider control model convergence countable space decomposition defined denote deterministic develop drift condition equation equivalent Ergodic Theorem exists f-regular Feller chains finite follows forward recurrence geometric ergodicity half line Harris recurrent hence holds initial condition invariant measure invariant probability measure kernel Lemma linear model lower semicontinuous m-skeleton Markov chain Markov property Markovian matrix NSS(F Nummelin open set petite set Poisson's equation positive Harris positive recurrent probability measure PROOF Proposition prove queue random variables random walk recurrence time chain recurrent chains result sample path satisfies Section sequence SETAR model space model split chain stability stochastic strongly aperiodic subinvariant Suppose that Þ T-chain test function theory topological transition probability Tweedie uniformly transient σα Φη Φο