BAHSOUN, W. and GORA, P., 2005. Position-dependent random maps in one and higher dimensions. Studia Mathematica, 166 (3), pp.271-286.
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. We study random maps with position dependent probabilities on the interval and on a bounded domain of Rn. Sufficient conditions for the existence of an absolutely continuous invariant measure for a random map with position dependent probabilities on the interval and on a bounded domain of Rn are the main results.
The research of P.G. was supported by NSERC grant. W.B. is a recipient of PIMS