Théorème de renouvellement pour chaînes de Markov fortement ergodiques : application aux modèles itératifs lipschitziens

Abstract

Let Q be a transition probability on a measurable space E. Let ( X n ) n ∈ N be a stationary Markov chain associated to Q. Let ξ : E → R measurable. Under a moment condition of order 1 + ε on ξ and under functional hypotheses on the action of Q and the Fourier kernels associated to ( Q , ξ ) , on a certain Banach space, we establish a renewal theorem for ( ξ ( X n ) ) n ∈ N ∗ . We use Fourier techniques and a perturbation operator method based on a result by Keller–Liverani. An application to Lipschitz iterative models is given. To cite this article: D. Guibourg, C. R. Acad. Sci. Paris, Ser. I 346 (2008).