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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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https://hal.archives-ouvertes.fr/hal-00852716
Contributor : Olivier Durieu <>
Submitted on : Wednesday, August 21, 2013 - 11:59:47 AM
Last modification on : Thursday, February 7, 2019 - 2:45:12 PM

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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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