Central limit theorems for multiple Skorohod integrals

Ivan Nourdin (1) , David Nualart (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 Department of Mathematics [Lawrence, Kansas]

In this paper, we prove a central limit theorem for a sequence of iterated Shorohod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit is a conditionally Gaussian random variable. Some applications to sequences of multiple stochastic integrals, and renormalized weighted Hermite variations of the fractional Brownian motion are discussed.

Mots clés: central limit theorem; fractional Brownian motion; Malliavin calculus

Domaines: Probabilités [math.PR]

Ivan Nourdin, David Nualart. Central limit theorems for multiple Skorohod integrals. 2009. ⟨hal-00164821v5⟩