Ergodicity of a measure-valued Markov chain induced by random transformations
type: Item
instance of: scholarly article
title: Ergodicity of a measure-valued Markov chain induced by random transformations
zbMATH Open document ID: 0621.60058
DOI: 10.1007/BF00334038
publication date: 1988-01-01T00:00:00Z
review text: Let \(Z_ 1,Z_ 2,..\). be a sequence of i.i.d. random transformations (possibly discontinuous) of a compact metric space M, and let E denote the space of normalized mass distributions on M. Given \(\mu\) in E, let \(\mu _ n\) denote the random measure \(\mu \circ (Z_ n\circ...\circ Z_ 1)^{-1}\) (when well-defined). We construct the transition probability P of the E-valued Markov chain \((\mu _ n)\), and give a necessary and sufficient condition for P to have a unique invariant measure concentrated on the degenerate mass distributions. Convergence to 'statistical equilibrium' of the associated discrete-time stochastic flow is investigated.
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 47A35
zbMATH DE Number: 4007370
zbMATH Keywords: unique invariant measure
zbMATH Keywords: random transformation
zbMATH Keywords: ergodicity
zbMATH Keywords: random ergodic theorem
zbMATH Keywords: stochastic flow
author: Richard W. R. Darling
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4007370