The Annals of Probability

Existence and Continuity of Occupation Densities of Stochastic Integral Processes

Peter Imkeller

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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


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