Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

How a centered random walk on the affine group goes to infinity

Auteur(s):

Code(s) de Classification MSC:

Résumé: We consider the processes obtained by (left and right) products of random i.i.d. affine transformations of the Euclidean space $\RR^d$. Our main goal is to describe the geometrical behavior at infinity of the trajectories of these processes in the most critical when the dilatation of the random affinities is centered. Then we derive a proof of the uniqueness of the invariant Radon measure for the Markov chain induced on $\RR^d$ by the left random walk and prove a stronger property of divergence for the process on induced by the right random walk.

Mots Clés: Random walk ; Affine group ; Random coefficient autoregressive model ; Limit theorem ; Stability

Date: 2001-05-15

Prépublication numéro: PMA-658

Postscript file (with figures) : PMA-658.ps