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.
Publié le : 1993-04-14
Classification:
Skorohod integral processes,
occupation densities,
Tanaka's formula,
Kolmogorov's continuity criterion,
60H05,
60G17,
60G48,
47B10
@article{1176989282,
author = {Imkeller, Peter},
title = {Existence and Continuity of Occupation Densities of Stochastic Integral Processes},
journal = {Ann. Probab.},
volume = {21},
number = {4},
year = {1993},
pages = { 1050-1072},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989282}
}
Imkeller, Peter. Existence and Continuity of Occupation Densities of Stochastic Integral Processes. Ann. Probab., Tome 21 (1993) no. 4, pp. 1050-1072. http://gdmltest.u-ga.fr/item/1176989282/