Absolutely continuous invariant measures for random maps

Abstract:
A random map is a discrete-time dynamical system in which one of a number of transformations is randomly selected and applied on each iteration of the process.
Such a system can model real life processes in which the mechanism of evolution can change randomly, for example market prices or biological systems in varying enviroments. In this presentation, we study random maps with position dependent probabilities on the interval and on a bounded domain of $\mathbb R^n$. We describe sufficient conditions for the existence of an absolutely continuous invariant measure for random map with position dependent probabilities on the interval and on a bounded domain of $\mathbb R^n$.