A probabilistic representation of constants in Kesten's renewal theorem

Nathanaël Enriquez (1) , Christophe Sabot (2) , Olivier Zindy (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 ICJ - Institut Camille Jordan

The aims of this paper are twofold. Firstly, we derive some probabilistic representation for the constant which appears in the one-dimensional case of Kesten's renewal theorem. Secondly, we estimate the tail of some related random variable which plays an essential role in the description of the stable limit law of one-dimensional transient sub-ballistic random walks in random environment.

Mots clés: Renewal series; coupling; fluctuation theory of random walks

Domaines: Probabilités [math.PR]

Nathanaël Enriquez, Christophe Sabot, Olivier Zindy. A probabilistic representation of constants in Kesten's renewal theorem. 2007. ⟨hal-00137772v1⟩