Markov Chains and Invariant Probabilities (Progress in Mathematics, 211, Band 211)

Hernández-Lerma, Onésimo and Jean B. Lasserre:

ISBN 10: 3764370009 / ISBN 13: 9783764370008

Editore: Birkhäuser 24.02.2003., 2003

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224 Seiten Mit leichten altersbedingten Lager- und Gebrauchsspuren. Biblitoheksex. U-25 Sprache: Englisch Gewicht in Gramm: 495 15,6 x 1,4 x 23,4 cm, Gebundene Ausgabe. Codice articolo 120649

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Titolo: Markov Chains and Invariant Probabilities (...

Casa editrice: Birkhäuser 24.02.2003.

Data di pubblicazione: 2003

Legatura: Rilegato

Condizione: Gut

Edizione: Auflage: 2003.

Descrizione articolo

Riassunto:

This 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).

Recensione:

"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