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