Occupation densities for certain processes related to fractional Brownian motion

Khalifa Es-Sebaiy (1) , David Nualart (2) , Youssef Ouknine (1) , Ciprian A. Tudor (3)

1 Département de mathématiques [FSSM]
2 Department of Mathematics [Lawrence, Kansas]
3 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

In this paper we establish the existence of a square integrable occupation density for two classes of stochastic processes. First we consider a Gaussian process with an absolutely continuous random drift, and secondly we handle the case of a (Skorohod) integral with respect to the fractional Brownian motion with Hurst parameter $H>\frac 12$. The proof of these results uses a general criterion for the existence of a square integrable local time, which is based on the techniques of Malliavin calculus.

Domaines: Probabilités [math.PR]

Khalifa Es-Sebaiy, David Nualart, Youssef Ouknine, Ciprian A. Tudor. Occupation densities for certain processes related to fractional Brownian motion. Stochastics: An International Journal of Probability and Stochastic Processes, 2010, 82 (2), pp.133-147. ⟨10.1080/17442500903045531⟩. ⟨hal-00211827⟩