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

### Penalization of the Wiener measure and principal values

Auteur(s):

Code(s) de Classification MSC:

• 60F05 Central limit and other weak theorems
• 60J55 Local time and additive functionals

Résumé: Consider the law $\q_\epsilon^{(\mu)}$ which is absolutely continuous with respect to the Wiener measure, with density ${\math D}_t= \exp\big(\int_0^t h(B_s) dB_s - {1\over2} \int_0^t h^2(B_s) ds\big)$ and $h ={\mu\over x}\i_{(|x|\ge \epsilon)}$. When $\mu \ge 1/2$, we show that as $\epsilon\to0_+$, there exists a penalization effect'' of the Wiener measure through the densities ${\math D}_t$, such that the limit law does not charge the paths hitting $0$. The remaining case $\mu < 1/2$ together with a more general form of $h$ are also studied.

Mots Clés: Penalization ; principal value

Date: 2000-05-22

Prépublication numéro: PMA-594