Invariant measures for random dynamical systems

Volume 451 / 2008

Katarzyna Horbacz Dissertationes Mathematicae 451 (2008), 1-63 MSC: Primary 47A35, 60J05, 37A30; Secondary 37A50, 60J75, 11K55. DOI: 10.4064/dm451-0-1

Abstract

We consider random dynamical systems with randomly chosen jumps on Polish spaces. They generalize Markov processes corresponding to iterated function systems, Poisson driven stochastic differential equations, and irreducible Markov systems. We formulate criteria for the existence of an invariant measure and asymptotic stability for these systems. Estimates of the lower pointwise and concentration dimension of invariant measures are also given.

Authors

  • Katarzyna HorbaczInstitute of Mathematics
    Silesian University
    Bankowa 14
    40-007 Katowice, Poland
    e-mail

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