On the fourth moment theorem for the complex multiple Wiener-Itô integrals
arXiv:1408.1817 · doi:10.1142/S0219025717500059
Abstract
In this paper, a product formula of Hermite polynomials is given and then the relation between the real Wiener-Itô chaos and the complex Wiener-Itô 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-Itô multiple integrals is obtained.
29 pages