Stable convergence of multiple Wiener-Itô integrals

Giovanni Peccati (1) , Murad Taqqu (2)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 Department of Mathematics and Statistics [Boston]

We prove sufficient conditions, ensuring that a sequence of multiple Wiener-Itô integrals (with respect to a general Gaussian process) converges stably to a mixture of normal distributions. Our key tool is an asymptotic decomposition of contraction kernels, realized by means of increasing families of projection operators. We also use an infinite-dimensional Clark-Ocone formula, as well as a version of the correspondence between "abstract" and "concrete" filtered Wiener spaces, in a spirit similar to Üstünel and Zakai (1997).

Mots clés: Stable Convergence; Multiple Wiener-Itô Integrals; Projection Operators; Gaussian Processes

Domaines: Probabilités [math.PR]

Giovanni Peccati, Murad Taqqu. Stable convergence of multiple Wiener-Itô integrals. 2006. ⟨hal-00023360⟩