Let $I_p(f)$ and $I_q(g)$ be multiple Wiener-Ito integrals of order $p$ and $q$, respectively. A characterization of independence of general random variables on Wiener space in the context of the stochastic calculus of variations is derived and a necessary and sufficient condition on the pair of kernels $(f, g)$ is derived under which the random variables $I_p(f), I_q(g)$ are independent.
Publié le : 1989-10-14
Classification:
Independence,
Wiener chaos,
multiple Wiener-Ito integrals,
the Malliavin calculus,
60H07,
60H05,
60J65
@article{1176991164,
author = {Ustunel, Ali Suleyman and Zakai, Moshe},
title = {On Independence and Conditioning On Wiener Space},
journal = {Ann. Probab.},
volume = {17},
number = {4},
year = {1989},
pages = { 1441-1453},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991164}
}
Ustunel, Ali Suleyman; Zakai, Moshe. On Independence and Conditioning On Wiener Space. Ann. Probab., Tome 17 (1989) no. 4, pp. 1441-1453. http://gdmltest.u-ga.fr/item/1176991164/