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Marche aléatoire sur le semi-groupe des contractions de $${\mathbb{R}}^ d$$. Cas de la marche aléatoire sur $${\mathbb{R}}_ +$$ avec choc élastique en zero. (Random walk on the semigroup of contractions of $$R^ d$$. Case of the random walk with elastic shock in zero on $${\mathbb{R}}_ +)$$. (French) Zbl 0632.60007
The author considers the Markov chain $$\{X_ n$$, $$n\geq 0\}$$ on $$R^ d$$ defined by $$X_ 0(x)=x$$ and $$X_ n(x)=Y_ n\circ...\circ Y_ 1(x)$$, $$n\geq 1$$, where the law of the i.i.d. random elements $$\{Y_ n$$, $$n\geq 1\}$$ has support on some subclass of Lipschitz functions. Under some conditions, existence of the invariant measure is proved. Applications to the random walk on $$R^+$$ are given.
Reviewer: R.Norvaiša
##### MSC:
 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization 60G50 Sums of independent random variables; random walks 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
##### Keywords:
Lipschitz functions; invariant measure