Author | Hernรกndez-Lerma, Onรฉsimo. author |
---|---|

Title | Markov Chains and Invariant Probabilities [electronic resource] / by Onรฉsimo Hernรกndez-Lerma, Jean Bernard Lasserre |

Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2003 |

Connect to | http://dx.doi.org/10.1007/978-3-0348-8024-4 |

Descript | XVI, 208 p. online resource |

SUMMARY

This book concerns discrete-time homogeneous Markov chains that admit an invariant probability measure. The main objective is to give a systematic, self-contained presentation on some key issues about the ergodic behavior of that class of Markov chains. These issues include, in particular, the various types of convergence of expected and pathwise occupation measures, and ergodic decompositions of the state space. Some of the results presented appear for the first time in book form. A distinguishing feature of the book is the emphasis on the role of expected occupation measures to study the long-run behavior of Markov chains on uncountable spaces. The intended audience are graduate students and researchers in theoretical and applied probability, operations research, engineering and economics

CONTENT

1 Preliminaries -- 1.1 Introduction -- 1.2 Measures and Functions -- 1.3 Weak Topologies -- 1.4 Convergence of Measures -- 1.5 Complements -- 1.6 Notes -- I Markov Chains and Ergodicity -- 2 Markov Chains and Ergodic Theorems -- 3 Countable Markov Chains -- 4 Harris Markov Chains -- 5 Markov Chains in Metric Spaces -- 6 Classification of Markov Chains via Occupation Measures -- II Further Ergodicity Properties -- 7 Feller Markov Chains -- 8 The Poisson Equation -- 9 Strong and Uniform Ergodicity -- III Existence and Approximation of Invariant Probability Measures -- 10 Existence of Invariant Probability Measures -- 11 Existence and Uniqueness of Fixed Points for Markov Operators -- 12 Approximation Procedures for Invariant Probability Measures

Mathematics
Operations research
Management science
Probabilities
Physics
Mathematics
Probability Theory and Stochastic Processes
Operations Research Management Science
Mathematical Methods in Physics