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Complex Wiener-Itô Chaos Decomposition Revisited

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Abstract

In this article, some properties of complex Wiener-Itô 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-Itô multiple integrals are given.

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Correspondence to Yong Chen or Yong Liu.

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Dedicated to our supervisor Professor Minping Qian on her 80th birthday

Supported by NSFC (11871079) and NSFC (11731009) and Center for Statistical Science, PKU.

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Chen, Y., Liu, Y. Complex Wiener-Itô Chaos Decomposition Revisited. Acta Math Sci 39, 797–818 (2019). https://doi.org/10.1007/s10473-019-0311-6

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  • DOI: https://doi.org/10.1007/s10473-019-0311-6

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