Markov Chains and Invariant Probabilities

Softcover Nachdruck of the original 1. Auflage 2003
ISBN: 978-3-0348-9408-1
Verlag: Birkhäuser Basel

Buch, Englisch, Band 211, 208 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 353 g

Reihe: Progress in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Lasserre, Jean B.

Hernández-Lerma, Onésimo

Fachgebiete

• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensforschung
• Mathematik | Informatik Mathematik Stochastik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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.