Strong Unique Ergodicity of Random Dynamical Systems on Polish Spaces

Paweł Płonka

doi:10.1515/amsil-2016-0002

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Strong Unique Ergodicity of Random Dynamical Systems on Polish Spaces

Annales Mathematicae Silesianae

Volume 30 (2016): Issue 1 (September 2016)

By: Paweł Płonka

Open Access

|Sep 2016

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].

References

[1] Arnold L., Random dynamical systems, Springer Monographs in Mathematics, Springer, Berlin, 1998.10.1007/978-3-662-12878-7
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[2] Crauel H., Random probability measures on Polish spaces, Series Stochastics Monographs, Vol. 11, Taylor & Francis, London, 2002.10.1201/b12601
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[3] Crauel H., Flandoli F., Attractors for random dynamical systems, Probab. Theory Relat. Fields 100 (1994), 365–393.10.1007/BF01193705
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[4] Lasota A., Yorke J.A., Lower bound technique for Markov operators and iterated function systems, Random Comput. Dynam. 2 (1994), 41–77.
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[5] Szarek T., The stability of Markov operators on Polish spaces, Studia Math. 143 (2000), 145–152.10.4064/sm-143-2-145-152
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[6] Szarek T., Invariant measures for non-expansive Markov operators on Polish spaces, Dissertationes Math. 415 (2003), 62 pp.10.4064/dm415-0-1
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[7] Valadier M., Young measures, in: Methods of Nonconvex Analysis (Varrenna 1989), Lecture Notes in Math. 1446, Springer, Berlin, 1990, pp. 152–188.
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Articles in this issue

DOI: https://doi.org/10.1515/amsil-2016-0002 | Journal eISSN: 2391-4238 (formerly 0860-2107) | Journal ISSN: 0860-2107

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Language: English

Page range: 129 - 142

Submitted on: May 22, 2015

Published on: Sep 23, 2016

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Keywords:

random dynamical systems,

invariant measures,

asymptotic stability

MSC:

37H99,

37B25,

47B80,

60H25

Related subjects:

Mathematics,

General mathematics

© 2016 Paweł Płonka, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 30 (2016): Issue 1 (September 2016)