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On the fourth moment theorem for complex multiple Wiener–Itô integrals

School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, P. R. China

E-mail Address: chenyong77@gmail.com

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and

Yong Liu

LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China

E-mail Address: liuyong@math.pku.edu.cn

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https://doi.org/10.1142/S0219025717500059Cited by:4 (Source: Crossref)

Abstract

In this paper, we give a product formula of Hermite polynomials and a relation between real Wiener–Itô chaos and complex Wiener–Itô chaos is shown. By this relation and the known multivariate extension of the fourth moment theorem for real multiple integrals, a fourth moment theorem (the Nualart–Peccati criterion) for complex Wiener–Itô multiple integrals is obtained.

Communicated by S. Luo

Keywords:

AMSC: 60F05, 60H05, 60H07, 60G15

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