COMPLEX WIENER-ITO CHAOS DECOMPOSITION REVISITED  

作　　者：Yong CHEN Yong UU 陈勇;刘勇(College of Mathematics and Information Science,Jiangxi Normal University,Nanchang 330022,China;LMAM School of Mathematical Sciences,Peking University,Beijing 100871,China)

机构地区：[1]College of Mathematics and Information Science,Jiangxi Normal University,Nanchang 330022,China [2]LMAM School of Mathematical Sciences,Peking University,Beijing 100871,China

出　　处：《Acta Mathematica Scientia》2019年第3期797-818,共22页数学物理学报（B辑英文版）

基　　金：Supported by NSFC(11871079);NSFC (11731009);Center for Statistical Science,PKU

摘　　要：In this article, some properties of complex Wiener-It? 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-It? multiple integrals are given.In this article, some proper ties of complex Wiener-Ito multiple integrals and complex Ornstein-Uhlenbeck opera tors 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-Ito multiple integrals are given.

关 键 词：Complex Hermite polynomials complex Gaussian isonormal processes complex Wiener-Ito Multiple Integrals complex Ornstein-Uhlenbeck operators and semigroups 

分 类 号：O[理学]