Séminaire de Probabilités et Statistique :

Le 09 octobre 2006 à 10:30 - UM2 - Bât 09

Présentée par Eddahbi M'hamed - Université Cadi Ayyad (Marrakech)

"Developpement en chaos de Wiener du temps local du mouvement Brownien Fractionnaire et applications"

We give the Wiener-Itô chaotic decomposition for the local time of the d-dimensional fractional Brownian motion with N-parameters. We study its smoothness in the Sobolev--Watanabe spaces and the asymptotic behavior in Sobolev norm of the local time of the d-dimensional fractional Brownian motion with N-parameters when the space variable tends to zero, both for the fixed time case and when simultaneously time tends to infinity and space variable to zero. In the one dimensional case, other applications for some additive functionals of the fractional Brownian motion that arise as limits in law of some occupation times of this process are also studied. In concrete, this functionals are obtained via the Cauchy principal value and the Hadamard finite part. We derive some regularity properties of theses functionals in Sobolev-Watanabe sense. * Related works with R. Lacayo, J.L. Solé J. Vives and C.A. Tudor