Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### The most visited sites of symmetric stable processes

Auteur(s):

Code(s) de Classification MSC:

• 60J55 Local time and additive functionals

Résumé: Let $X_t$ be a symmetric stable process of index $\alpha\in (1,2]$. Let $V_t$ be the value of $x$ at which the local time at time $t$ takes its maximum. We prove that $V_t$ is transient, and give an estimate for the rate of escape. Our method is to use a type of Ray-Knight theorem for the local times of stable processes and some estimates for fractional Brownian motion.

Mots Clés: Local time; stable process; most visited site; Dynkin's isomorphism theorem; fractional Brownian motion

Date: 1999-01-10

Prépublication numéro: PMA-479