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

### On local times of a symmetric stable process as a doubly-indexed process

Auteur(s):

Code(s) de Classification MSC:

• 60F25 $L^p$-limit theorems
• 60H05 Stochastic integrals
• 60J55 Local time and additive functionals

Résumé: We consider the local time process $(L^x_t, x\in \R,t\geq 0)$ of a symmetric stable process $X$ with an index $\beta$ in $(1,2]$. We compute the p-variation of $L$ on any rectangle of $\R \times [0,\infty)$. Unlike for the p-variation of $L$ with respect to the spatial parameter (studied by Marcus and Rosen (1992b)), we show here that the Brownian case, i.e., when $\beta = 2$, is atypical .

Mots Clés: Itô formula ; local time ; p-variation ; symmetric stable process

Date: 1999-10-04

Prépublication numéro: PMA-535