Department of Mathematics & Statistics,

Concordia University,

7141 Sherbrooke Street West,

Montreal, Quebec,

CANADA H4B 1R6

E-mail: pgora@vax2.concordia.ca

**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 $\mathbb
R^n$.