Existence and Continuity of Occupation Densities of Stochastic Integral Processes

Abstract

Let $f$ be a square-integrable function on the unit square. Assume that the singular numbers $(a_i)_{i \in \mathbb{N}}$ of the Hilbert-Schmidt operator associated with $f$ admit some $0 < \alpha < \frac{1}{3}$ such that $\sum^\infty_{i = 1}|a_i|^\alpha < \infty$. We present a purely stochastic method to investigate the occupation densities of the Skorohod integral process $U$ induced by $f$. It allows us to show that $U$ possesses continuous square-integrable occupation densities and obviously generalizes beyond the second Wiener chaos.