We consider a family of transformations with a random parameter and study a random dynamical system in which one transformation is randomly selected from the family and applied on each iteration. The parameter space may be of cardinality continuum. Further, the selection of the transformation need not be independent of the position in the state space. We show the existence of absolutely continuous invariant measures for random maps on an interval under some conditions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-1-2,
author = {Tomoki Inoue},
title = {Invariant measures for position dependent random maps with continuous random parameters},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {11-29},
zbl = {1267.37054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-1-2}
}
Tomoki Inoue. Invariant measures for position dependent random maps with continuous random parameters. Studia Mathematica, Tome 209 (2012) pp. 11-29. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-1-2/