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Random dynamical systems with jumps

Part of: General theory of linear operators

Published online by Cambridge University Press:  14 July 2016

Katarzyna Horbacz
Katarzyna Horbacz*
Affiliation:
University of Silesia
*
∗ Postal address: Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland. Email address: horbacz@ux2.math.us.edu.pl
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Abstract

We consider random dynamical systems with randomly chosen jumps on infinite-dimensional spaces. The choice of deterministic dynamical systems and jumps depends on a position. The system generalizes dynamical systems corresponding to learning systems, Poisson driven stochastic differential equations, iterated function system with infinite family of transformations and random evolutions. We will show that distributions which describe the dynamics of this system converge to an invariant distribution. We use recent results concerning asymptotic stability of Markov operators on infinite-dimensional spaces obtained by T. Szarek.

Keywords

Dynamical systemMarkov semigroupinvariant measure

MSC classification

Primary: 47A35: Ergodic theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 3 , September 2004 , pp. 890 - 910
Copyright
Copyright © Applied Probability Trust 2004 

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