Complex Wiener-It\^o Chaos Decomposition Revisited

Yong Chen; Yong Liu

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Complex Wiener-It\^o Chaos Decomposition Revisited

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arxiv 1902.09111 v1 pith:WFDHQV45 submitted 2019-02-25 math.PR

Yong CHEN , Yong LIU This is my paper · ORCID

classification math.PR

keywords complexformulawiener-itintegralsmultipleornstein-uhlenbecksemigroupsapplication

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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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