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 Emphasis on the role of expected occupation measures to study the long-run behavior of Markov chains on uncountable spaces

Autorentext

Onésimo Hernández-Lerma received the Science and Arts National Award from the Government of MEXICO in 2001, an honorary doctorate from the University of Sonora in 2003, and the Scopus Prize from Elsevier in 2008. Xianping Guo received the He-Pan-Qing-Yi Best Paper Award from the 7th Word Congress on Intelligent Control and Automation in 2008.

Inhalt
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.