# Empirical processes of iterated maps that contract on average

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 $\sum_i d(T_ix,T_iy)p_i(x) < \rho d(x,y)$ for some $\rho<1$. In the present note, we study the weak convergence of the empirical process associated to this Markov chain.
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Article dans une revue
Statistics and Probability Letters, Elsevier, 2013, 83 (11), pp.2454-2458. 〈10.1016/j.spl.2013.07.003〉
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https://hal.archives-ouvertes.fr/hal-00852716
Contributeur : Olivier Durieu <>
Soumis le : mercredi 21 août 2013 - 11:59:47
Dernière modification le : jeudi 7 février 2019 - 14:45:12

### Citation

Olivier Durieu. Empirical processes of iterated maps that contract on average. Statistics and Probability Letters, Elsevier, 2013, 83 (11), pp.2454-2458. 〈10.1016/j.spl.2013.07.003〉. 〈hal-00852716〉

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