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arXiv · 1408.1817

On the fourth moment theorem for the complex multiple Wiener-It\^{o} integrals

Yong Chen·Yong Liu
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Abstract

In this paper, a product formula of Hermite polynomials is given and then the relation between the real Wiener-It\^{o} chaos and the complex Wiener-It\^{o} chaos (or: multiple integrals) is shown. By this relation and the known multivariate extension of the fourth moment theorem for the real multiple integrals, the fourth moment theorem (or say: the Nualart-Peccati criterion) for the complex Wiener-It\^{o} multiple integrals is obtained.

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BibTeXRIS

Yong Chen, Yong Liu. 2014-08-08. On the fourth moment theorem for the complex multiple Wiener-It\^{o} integrals. https://doi.org/10.1142/s0219025717500059

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