Markov Chains and Invariant Probabilities von Onésimo Hernández-Lerma | ISBN 9783034880244

Markov Chains and Invariant Probabilities

von Onésimo Hernández-Lerma und Jean B. Lasserre
Mitwirkende
Autor / AutorinOnésimo Hernández-Lerma
Autor / AutorinJean B. Lasserre
Buchcover Markov Chains and Invariant Probabilities | Onésimo Hernández-Lerma | EAN 9783034880244 | ISBN 3-0348-8024-3 | ISBN 978-3-0348-8024-4

"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

Markov Chains and Invariant Probabilities

von Onésimo Hernández-Lerma und Jean B. Lasserre
Mitwirkende
Autor / AutorinOnésimo Hernández-Lerma
Autor / AutorinJean B. Lasserre
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).