Empirical processes of iterated maps that contract on average

Olivier Durieu

paper

Empirical processes of iterated maps that contract on average

arXiv:1206.4903

Abstract

We consider a Markov chain obtained by random iterations of Lipschitz maps $T_{i}$ chosen with a probability $p_{i} (x)$ depending on the current position $x$ . We assume this system has a property of "contraction on average", that is $\sum_{i} d (T_{i} x, T_{i} y) p_{i} (x) < ρ d (x, y)$ for some $ρ < 1$ . In the present note, we study the weak convergence of the empirical process associated to this Markov chain.