Random dynamical systems with jumps and with a function type intensity

Joanna Kubieniec

Published: 2016-09-23

Vol. 30 (2016)

Random dynamical systems with jumps and with a function type intensity

Joanna Kubieniec

Abstract

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

Download files

PDF

Citation rules

Kubieniec, J. (2016). Random dynamical systems with jumps and with a function type intensity. Annales Mathematicae Silesianae, 30, 63–87. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13956

Similar Articles

Katarzyna Oczkowicz, Asymptotic stability of Markov operators corresponding to the dynamical systems with multiplicative perturbations , Annales Mathematicae Silesianae: Vol. 7 (1993)
Jason Bentley, Piotr Mikusiński, Transfunctions applied to plans, Markov operators and optimal transport , Annales Mathematicae Silesianae: 2024: Online First
Józef Kalinowski, On invertible preservers of singularity and nonsingularity of matrices over a field , Annales Mathematicae Silesianae: Vol. 24 (2010)
Lanzhe Liu, The continuity of multilinear integral operators on Morrey spaces , Annales Mathematicae Silesianae: Vol. 20 (2006)
Paweł Płonka, Strong unique ergodicity of random dynamical systems on Polish spaces , Annales Mathematicae Silesianae: Vol. 30 (2016)
Maciej Ślęczka, Exponential convergence for Markov systems , Annales Mathematicae Silesianae: Vol. 29 (2015)
Liliana Rybarska-Rusinek, String stability of singularly perturbed stochastic systems , Annales Mathematicae Silesianae: Vol. 16 (2002)
Jerzy Klamka, Controllability of infinite-dimensional systems with delays in control , Annales Mathematicae Silesianae: Vol. 1 (1985)
Ryszard Rudnicki, With Andrzej Lasota there and back again , Annales Mathematicae Silesianae: Vol. 38 No. 2 (2024)
Joanna Kubieniec, Central limit theorem for random dynamical system with jumps and state-dependent jump intensity , Annales Mathematicae Silesianae: 2024: Online First

1 2 3 4 5 6 7 > >>

You may also start an advanced similarity search for this article.

References

1. Davis M.H.A., Markov Models and Optimization, Chapman and Hall, London, 1993.
2. Diekmann O., Heijmans H.J., Thieme H.R., On the stability of the cells size distribution, J. Math. Biol. 19 (1984), 227–248.
3. Horbacz K., Asymptotic stability of a system of randomly connected transformations on Polish spaces, Ann. Polon. Math. 76 (2001), 197–211.
4. Horbacz K., Invariant measures for random dynamical systems, Dissertationes Math. 451 (2008), 68 pp.
5. Kazak J., Piecewise-deterministic Markov processes, Annales Polonici Mathematici 109 (2013), 279–296.
6. Lasota A., Yorke J.A., Lower Bound technique for Markov operators and iterated function systems, Random Comput. Dynam. 2 (1994), 41–77.
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.
8. Snyder D., Random Point Processes, Wiley, New York, 1975.
9. Szarek T., Invariant measures for nonexpansive Markov operators on Polish spaces, Dissertationes Math. 415 (2003), 62 pp. Google Scholar

Vol. 30 (2016)
Published: 2016-09-23

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

Submit