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Annales Mathematicae Silesianae

Editor-in-Chief: Sablik, Maciej

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Strong Unique Ergodicity of Random Dynamical Systems on Polish Spaces

Paweł Płonka
Published Online: 2016-09-23 | DOI: https://doi.org/10.1515/amsil-2016-0002


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: random dynamical systems; invariant measures; asymptotic stability

MSC 2010: 37H99; 37B25; 47B80; 60H25


  • [1] Arnold L., Random dynamical systems, Springer Monographs in Mathematics, Springer, Berlin, 1998.Google Scholar

  • [2] Crauel H., Random probability measures on Polish spaces, Series Stochastics Monographs, Vol. 11, Taylor & Francis, London, 2002. Google Scholar

  • [3] Crauel H., Flandoli F., Attractors for random dynamical systems, Probab. Theory Relat. Fields 100 (1994), 365–393.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.Google Scholar

  • [5] Szarek T., The stability of Markov operators on Polish spaces, Studia Math. 143 (2000), 145–152.Google Scholar

  • [6] Szarek T., Invariant measures for non-expansive Markov operators on Polish spaces, Dissertationes Math. 415 (2003), 62 pp. 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.Google Scholar

About the article

Received: 2015-05-22

Revised: 2016-02-29

Published Online: 2016-09-23

Published in Print: 2016-09-01

Citation Information: Annales Mathematicae Silesianae, Volume 30, Issue 1, Pages 129–142, ISSN (Online) 0860-2107, DOI: https://doi.org/10.1515/amsil-2016-0002.

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© 2016 Paweł Płonka, published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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