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

Abstract

In this paper, we give a product formula of Hermite polynomials and a relation between real Wiener–Itô chaos and complex Wiener–Itô chaos is shown. By this relation and the known multivariate extension of the fourth moment theorem for real multiple integrals, a fourth moment theorem (the Nualart–Peccati criterion) for complex Wiener–Itô multiple integrals is obtained.