Applications of a generalized metric in the analysis of iterated function systems

Iterated function systems make up an interesting class of stochastic processes which are useful for many types of stochastic modeling. In this paper we review and slightly generalize a contractivity condition guaranteeing uniqueness of invariant measures. Also, we examine how the invariant measure, and thus also the asymptotic behavior, of such a process is affected by perturbations of the defining functions and probabilities. Copyright Springer-Verlag Berlin/Heidelberg 2003