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:**

- 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*