Acta Mathematica Scientia

, Volume 39, Issue 3, pp 797–818 | Cite as

Complex Wiener-Itô Chaos Decomposition Revisited

  • Yong ChenEmail author
  • Yong LiuEmail author


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 

2010 MR Subject Classification

60H07 60F25 62M090 


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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceJiangxi Normal UniversityNanchangChina
  2. 2.LMAM, School of Mathematical SciencesPeking UniversityBeijingChina

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