数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (3): 797-818.doi: 10.1007/s10473-019-0311-6

• 论文 • 上一篇    下一篇

COMPLEX WIENER-ITÔ CHAOS DECOMPOSITION REVISITED

陈勇1, 刘勇2   

  1. 1. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China;
    2. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
  • 收稿日期:2018-09-28 修回日期:2018-12-03 出版日期:2019-06-25 发布日期:2019-06-27
  • 作者简介:Yong CHEN,E-mail:zhishi@pku.org.cn,chenyong77@gmail.comYong LIU,E-mail:liuyong@math.pku.edu.cn
  • 基金资助:
    Supported by NSFC (11871079) and NSFC (11731009) and Center for Statistical Science, PKU.

COMPLEX WIENER-ITÔ CHAOS DECOMPOSITION REVISITED

Yong CHEN1, Yong LIU2   

  1. 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:2018-09-28 Revised:2018-12-03 Online:2019-06-25 Published:2019-06-27
  • Supported by:
    Supported by NSFC (11871079) and NSFC (11731009) and Center for Statistical Science, PKU.

摘要: 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.

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

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

中图分类号: 

  • 60H07