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

### A LDP related to the strong arc-sine law

Auteur(s):

Code(s) de Classification MSC:

• 60F10 Large deviations
• 60J55 Local time and additive functionals
Résumé: We show a large deviations principle for the family of random variables $\{\frac{1}{t}\int _0 ^t \1_{B_u > 0}\ du\}$ when $t\to+\infty$, where $B= (B_u , u \geq 0)$ is a standard linear Brownian motion.