COMPLEX WIENER-ITÔ CHAOS DECOMPOSITION REVISITED

doi:10.1007/s10473-019-0311-6

Abstract

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.

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

CLC Number:

60H07

Yong CHEN, Yong LIU. COMPLEX WIENER-ITÔ CHAOS DECOMPOSITION REVISITED[J].Acta mathematica scientia,Series B, 2019, 39(3): 797-818.

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