Abstract
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.
Citation
Ali Suleyman Ustunel. Moshe Zakai. "On Independence and Conditioning On Wiener Space." Ann. Probab. 17 (4) 1441 - 1453, October, 1989. https://doi.org/10.1214/aop/1176991164
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