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arXiv:1408.1817 [math.PR]AbstractReferencesReviewsResources

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

Yong Chen, Yong Liu

Published 2014-08-08Version 1

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.

Comments: 29 pages
Categories: math.PR
Subjects: 60F05, 60H05, 60H07, 60G15
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