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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
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)