English

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

R2 v1 2026-06-22T05:23:04.665Z