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.
@book{bwmeta1.element.bwnjournal-rm-doi-10_4064-dm451-0-1,
author = {Katarzyna Horbacz},
title = {Invariant measures for random dynamical systems},
series = {GDML\_Books},
year = {2008},
zbl = {1157.37003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm451-0-1}
}
Katarzyna Horbacz. Invariant measures for random dynamical systems. GDML_Books (2008), http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm451-0-1/