Journal of Applied Mathematics and Stochastic Analysis 
Volume 2005 (2005), Issue 2, Pages 133-141
doi:10.1155/JAMSA.2005.133

A generalization of Straube's theorem: existence of absolutely continuous invariant measures for random maps

Md. Shafiqul Islam, Pawel Góra, and Abraham Boyarsky

 Department of Mathematics and Statistics, Concordia University, 7141 Sherbrooke Street West , Quebec, Montreal H4B 1R6, Canada
Received 29 February 2004; Revised 1 September 2004

Abstract

A random map is a discrete-time dynamical system in which one of a number of transformations is randomly selected and applied at each iteration of the process. In this paper, we study random maps. The main result provides a necessary and sufficient condition for the existence of absolutely continuous invariant measure for a random map with constant probabilities and position-dependent probabilities.