Asymptotic behaviors of randomly perturbed dynamical systems

Abstract

We consider the asymptotic behaviors of certain Markov processes which are generated by successive iterations of independent and identically distributed random maps. For the cases that after some number of iterations, iterated maps are Lipschitzian or satisfy the average contraction condition, we find sufficient conditions under which there exists a urique invariant probability. A functional central limit theorem and a strong law of large numbers are proved for Lipschitzian functions.