## Markov Chains and Stochastic StabilityMeyn 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 |

567 | |

587 | |

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### Common terms and phrases

A G B(X absorbing set analysis aperiodic assumption atom bounded in probability chain Q Chapter CM(F compact set consider control model countable space decomposition deﬁned deﬁnition denote deterministic develop drift condition equation equivalent Ergodic Theorem exists f-regular Feller chains ﬁnd ﬁnite ﬁrst ﬁxed follows forward recurrence function f G Z+ G Z1 G ZJF 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 NSS(F Nummelin open set petite set positive Harris positive recurrent probability measure PROOF Proposition prove Q is w-irreducible queue random variables random walk recurrence time chain recurrent chains result sample path satisﬁes Section sequence SETAR model space model speciﬁc split chain stability stochastic strongly aperiodic sufﬁciently Suppose that Q T-chain test function theory topological transition probability Tweedie uniformly transient V-uniformly ergodic