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

Fractional Brownian motions as "higher-order" fractional derivatives of Brownian local times

Auteur(s):

Code(s) de Classification MSC:

• 60J55 Local time and additive functionals
Résumé: Fractional derivatives ${\cal D}^\gamma$ of Brownian local times are well defined for all $\gamma<3/2$. We show that, in the weak convergence sense, these fractional derivatives admit themselves derivatives which feature all fractional Brownian motions. Strong approximation results are also developed as counterparts of limit theorems for Brownian additive functionals which feature the fractional derivatives of Brownian local times.