Occupation densities for certain processes related to fractional Brownian motion

TL;DR

This paper proves the existence of square integrable occupation densities for certain Gaussian processes, including those with random drift and fractional Brownian motion, using Malliavin calculus techniques.

Contribution

It introduces new conditions under which occupation densities exist for processes related to fractional Brownian motion, expanding the theoretical understanding.

Findings

Existence of occupation densities for Gaussian processes with random drift

Existence of occupation densities for Skorohod integrals with fractional Brownian motion (H>1/2)

Application of Malliavin calculus to establish these results

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 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.