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Complex Wiener-Itô Chaos Decomposition Revisited

Published 25 Feb 2019 in math.PR | (1902.09111v1)

Abstract: In this article, some properties of complex Wiener-It^o multiple integrals and complex Ornstein-Uhlenbeck operators and semigroups are obtained. Those include Stroock's formula, Hu-Meyer formula, Clark-Ocone formula and the hypercontractivity of complex Ornstein-Uhlenbeck semigroups. As an application, several expansions of the fourth moments of complex Wiener-It^o multiple integrals are given.

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