Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**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*