Continuous Dependence in a Problem of Convergence of Random Iteration

Abstract We show that an invariant measure of a Markov operator is contracting in the Hutchison distance, acting on space Borel probability measures Polish space, depends continuously given operator. In addition, we establish estimate for distance between measures. Some applications to weak limit iterates random-valued functions (in particular, so-called random affine maps, occuring, e.g., perpetuities analysis) are also given.