## The Annals of Probability

### Existence and Continuity of Occupation Densities of Stochastic Integral Processes

Peter Imkeller

#### 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.

#### Article information

Source
Ann. Probab., Volume 21, Number 2 (1993), 1050-1072.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176989282

Digital Object Identifier
doi:10.1214/aop/1176989282

Mathematical Reviews number (MathSciNet)
MR1217580

Zentralblatt MATH identifier
0779.60050

JSTOR