Relations de récurrence à coefficients aléatoires et lois stables

Abstract

We consider a multivariate affine stochastic recursion and the corresponding Birkhoff sum along a trajectory. Under a condition on the law of coefficients which is generic, we show that the above sum, suitably normalized, converges in distribution to a stable law, depending essentially on the multiplicative part of the relation. The proof is based on the spectral properties of the associated Markov operator, and on the homogeneity at infinity of the stationary measure.