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OverviewThis book is about discrete-time, time-homogeneous, Markov chains (Mes) and their ergodic behavior. To this end, most of the material is in fact about stable Mes, by which we mean Mes that admit an invariant probability measure. To state this more precisely and give an overview of the questions we shall be dealing with, we will first introduce some notation and terminology. Let (X,B) be a measurable space, and consider a X-valued Markov chain ~. = {~k' k = 0, 1, ... } with transition probability function (t.pJ.) P(x, B), i.e., P(x, B) := Prob (~k+1 E B I ~k = x) for each x E X, B E B, and k = 0,1, .... The Me ~. is said to be stable if there exists a probability measure (p.m.) /.l on B such that (*) VB EB. /.l(B) = Ix /.l(dx) P(x, B) If (*) holds then /.l is called an invariant p.m. for the Me ~. (or the t.p.f. P). Full Product DetailsAuthor: Onésimo Hernández-Lerma , Jean B. LasserrePublisher: Birkhauser Verlag AG Imprint: Birkhauser Verlag AG Edition: Softcover reprint of the original 1st ed. 2003 Volume: 211 Dimensions: Width: 15.50cm , Height: 1.20cm , Length: 23.50cm Weight: 0.355kg ISBN: 9783034894081ISBN 10: 3034894082 Pages: 208 Publication Date: 23 October 2012 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents1 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.ReviewsIt 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 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 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 Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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