On the fourth moment theorem for the complex multiple Wiener-It\^{o} integrals
Probability
2017-02-28 v1
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.
Keywords
Cite
@article{arxiv.1408.1817,
title = {On the fourth moment theorem for the complex multiple Wiener-It\^{o} integrals},
author = {Yong Chen and Yong Liu},
journal= {arXiv preprint arXiv:1408.1817},
year = {2017}
}
Comments
29 pages