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

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

#### 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.

First Page:
Primary Subjects: 60H05
Secondary Subjects: 60G17, 60G48, 47B10
Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1176989282
JSTOR: links.jstor.org
Digital Object Identifier: doi:10.1214/aop/1176989282
Mathematical Reviews number (MathSciNet): MR1217580
Zentralblatt MATH identifier: 0779.60050