Occupation densities for certain processes related to fractional Brownian motion

Abstract

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 second, we handle the case of a (Skorohod) integral with respect to the fractional Brownian motion with Hurst parameter . 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.

Keywords:

• Malliavin calculus
• Skorohod integral
• local times
• (bi)fractional Brownian motion

2000 Mathematics Subject Classification::

• 60G12
• 60G15
• 60H05
• 60H07