## The Annals of Probability

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

### 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.

#### Article information

**Source**

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

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 60H05: Stochastic integrals

Secondary: 60G17: Sample path properties 60G48: Generalizations of martingales 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]

**Keywords**

Skorohod integral processes occupation densities Tanaka's formula Kolmogorov's continuity criterion

#### Citation

Imkeller, Peter. Existence and Continuity of Occupation Densities of Stochastic Integral Processes. Ann. Probab. 21 (1993), no. 2, 1050--1072. doi:10.1214/aop/1176989282. https://projecteuclid.org/euclid.aop/1176989282