Empirical processes of iterated maps that contract on average

We consider a Markov chain obtained by random iterations of Lipschitz maps Ti chosen with a probability pi(x) depending on the current position x. We assume this system has a property of “contraction on average”, that is ∑id(Tix,Tiy)pi(x)<ρd(x,y) for some ρ<1. In the present note, we study the weak convergence of the empirical process associated to this Markov chain.

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Year of publication:	2013
Authors:	Durieu, Olivier
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 83.2013, 11, p. 2454-2458
Publisher:	Elsevier
Subject:	Iterated random maps \| Markov chains \| Empirical processes \| Weak convergence

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://ebvufind01.dmz1.zbw.eu/10011039988