Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Annales Mathematicae Silesianae

Editor-in-Chief: Sablik, Maciej

1 Issue per year

Mathematical Citation Quotient (MCQ) 2016: 0.10

Open Access
See all formats and pricing
More options …

Random Dynamical Systems with Jumps and with a Function Type Intensity

Joanna Kubieniec
Published Online: 2016-09-23 | DOI: https://doi.org/10.1515/amsil-2016-0004


In paper [4] there are considered random dynamical systems with randomly chosen jumps acting on Polish spaces. The intensity of this process is a constant λ. In this paper we formulate criteria for the existence of an invariant measure and asymptotic stability for these systems in the case when λ is not constant but a Lipschitz function.

Keywords: dynamical systems; asymptotic stability; Markov operators

MSC 2010: 37A30; 60J75; 93D20


  • [1] Davis M.H.A., Markov Models and Optimization, Chapman and Hall, London, 1993.Google Scholar

  • [2] Diekmann O., Heijmans H.J., Thieme H.R., On the stability of the cells size distribution, J. Math. Biol. 19 (1984), 227–248.Google Scholar

  • [3] Horbacz K., Asymptotic stability of a system of randomly connected transformations on Polish spaces, Ann. Polon. Math. 76 (2001), 197–211.Google Scholar

  • [4] Horbacz K., Invariant measures for random dynamical systems, Dissertationes Math. 451 (2008), 68 pp. Google Scholar

  • [5] Kazak J., Piecewise-deterministic Markov processes, Annales Polonici Mathematici 109 (2013), 279–296.Web of ScienceGoogle Scholar

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

  • [7] Lipniacki T., Paszek P., Marciniak-Czochra A., Brasier A.R., Kimel M., Transcriptional stochasticity in gene expression, J. Theor. Biol. 238 (2006), 348–367.Google Scholar

  • [8] Snyder D., Random Point Processes, Wiley, New York, 1975.Google Scholar

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

About the article

Received: 2016-01-13

Revised: 2016-04-12

Accepted: 2016-04-19

Published Online: 2016-09-23

Published in Print: 2016-09-01

Citation Information: Annales Mathematicae Silesianae, Volume 30, Issue 1, Pages 63–87, ISSN (Online) 0860-2107, DOI: https://doi.org/10.1515/amsil-2016-0004.

Export Citation

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

Comments (0)

Please log in or register to comment.
Log in