• S. BROFFERIO

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