RANDOMLY CONNECTED DYNAMICAL SYSTEMS ON BANACH SPACES

Authors: Katarzyna Horbacz ^a; Tomasz Szarek ^b

Affiliations:	^a Institute of Mathematics, Silesian University, Katowice, Bankowa 14, Poland
	^b Institut of Mathematics, Polish Academy of Sciences, Katowice, Bankowa 14, Poland

DOI: 10.1081/SAP-100002100

Publication Frequency: 6 issues per year

Published in: journal

Stochastic Analysis and Applications, Volume 19, Issue 4 June 2001 , pages 519 - 543

Subjects: Statistics & Probability; Stochastic Models & Processes;

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Abstract

We give sufficient conditions for asymptotic stability of Markov operators governing the evolution of measures due to the action of randomly chosen dynamical systems on Banach spaces. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for a semigroup generated by the considered systems.

Keywords: Dynamical systems; Markov operator; Asymptotic stability

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RANDOMLY CONNECTED DYNAMICAL SYSTEMS ON BANACH SPACES

Abstract