Markov chains and invariant probabilities / Onésimo Hernández-Lerma, Jean Bernard Lasserre

... The material is incorporated in the following chapters: 1. Preliminaries. 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. 7. Feller Markov chains. 8. The Poisson equation. 9. Strong and uniform ergodicity. 10. Existence of invariant probability measures. 11. Existence and uniqueness of fixed points for invariant measures. At the end of the book we find a quite comprehensive up-to-date reference list, as well as an index, and list of abbreviations.

The book is carefully written, its contents and style show undoubtedly that Markov chains form a beautiful branch of modern stochastics and hence of modern mathematics. There are reasons to congratulate the authors for writing this excellent work. A wide spectrum of readers will benefit from the book, in particular, researchers and PhD students in the area of probability, analysis, optimization theory and dynamical systems.(zbMath)