Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (3): 797-818.doi: 10.1007/s10473-019-0311-6

• Articles • Previous Articles     Next Articles

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.

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
Trendmd