New sufficient conditions for the existence of an invariant measure for nonexpansive Markov operators defined on Polish spaces are presented. These criteria are applied to iterated function systems, stochastically perturbed dynamical systems and Poisson stochastic differential equations. We also estimate the Ledrappier version of capacity for invariant measures.
@book{bwmeta1.element.bwnjournal-rm-doi-10_4064-dm415-0-1,
author = {Tomasz Szarek},
title = {Invariant measures for nonexpansive Markov operators on Polish spaces},
series = {GDML\_Books},
year = {2003},
zbl = {1051.37005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm415-0-1}
}
Tomasz Szarek. Invariant measures for nonexpansive Markov operators on Polish spaces. GDML_Books (2003), http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm415-0-1/