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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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
Key words
- Complex Hermite polynomials
- complex Gaussian isonormal processes
- complex Wiener-Itô Multiple Integrals
- complex Ornstein-Uhlenbeck operators and semigroups