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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60J10 Markov chains with discrete parameter
- 60B15 Probability measures on groups, Fourier transforms, factorization
- 60J15 Random walks

**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