Articles

COMPLEX WIENER-ITÔ CHAOS DECOMPOSITION REVISITED

  • Yong CHEN ,
  • Yong LIU
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  • 1. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China;
    2. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China

Received date: 2018-09-28

  Revised date: 2018-12-03

  Online published: 2019-06-27

Supported by

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

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.

Cite this article

Yong CHEN , Yong LIU . COMPLEX WIENER-ITÔ CHAOS DECOMPOSITION REVISITED[J]. Acta mathematica scientia, Series B, 2019 , 39(3) : 797 -818 . DOI: 10.1007/s10473-019-0311-6

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