Markov Chains and Invariant Probabilities

"It should be stressed that an important part of the results presented is due to the authors... In the reviewer's opinion, this is an elegant and most welcome addition to the rich literature of Markov processes." --MathSciNet

• 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.