Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws

Ivan Nourdin (1) , Jan Rosinski (2)

1 IECN - Institut Élie Cartan de Nancy
2 Department of Mathematics [Tennessee]

We characterize the asymptotic independence of multiple Wiener-Itô integrals. As a consequence of this characterization, we derive the celebrated fourth moment theorem of Nualart and Peccati and other related results on the multivariate convergence of multiple Wiener-Itô integrals, that involve Gaussian and non Gaussian limits.

Domaines: Probabilités [math.PR]

Ivan Nourdin, Jan Rosinski. Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws. 2011. ⟨hal-00654259v1⟩