1. bookVolume 30 (2016): Issue 1 (September 2016)
Journal Details
License
Format
Journal
eISSN
2391-4238
First Published
01 Jan 1985
Publication timeframe
2 times per year
Languages
English
access type Open Access

Strong Unique Ergodicity of Random Dynamical Systems on Polish Spaces

Published Online: 23 Sep 2016
Volume & Issue: Volume 30 (2016) - Issue 1 (September 2016)
Page range: 129 - 142
Received: 22 May 2015
Journal Details
License
Format
Journal
eISSN
2391-4238
First Published
01 Jan 1985
Publication timeframe
2 times per year
Languages
English
Abstract

In this paper we want to show the existence of a form of asymptotic stability of random dynamical systems in the sense of L. Arnold using arguments analogous to those presented by T. Szarek in [6], that is showing it using conditions generalizing the notion of tightness of measures. In order to do that we use tightness theory for random measures as developed by H. Crauel in [2].

Keywords

MSC 2010

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[3] Crauel H., Flandoli F., Attractors for random dynamical systems, Probab. Theory Relat. Fields 100 (1994), 365–393.10.1007/BF01193705Search in Google Scholar

[4] Lasota A., Yorke J.A., Lower bound technique for Markov operators and iterated function systems, Random Comput. Dynam. 2 (1994), 41–77.Search in Google Scholar

[5] Szarek T., The stability of Markov operators on Polish spaces, Studia Math. 143 (2000), 145–152.10.4064/sm-143-2-145-152Search in Google Scholar

[6] Szarek T., Invariant measures for non-expansive Markov operators on Polish spaces, Dissertationes Math. 415 (2003), 62 pp.10.4064/dm415-0-1Search in Google Scholar

[7] Valadier M., Young measures, in: Methods of Nonconvex Analysis (Varrenna 1989), Lecture Notes in Math. 1446, Springer, Berlin, 1990, pp. 152–188.Search in Google Scholar

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