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.
Ann. Probab.
17(4):
1441-1453
(October, 1989).
DOI: 10.1214/aop/1176991164