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Journal Articles Statistics and Probability Letters Year : 2013

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.

Dates and versions

hal-00852716 , version 1 (21-08-2013)

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