Stein's method meets Malliavin calculus: a short survey with new estimates

Ivan Nourdin (1) , Giovanni Peccati (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 MODAL'X - Modélisation aléatoire de Paris X

We provide an overview of some recent techniques involving the Malliavin calculus of variations and the so-called ``Stein's method'' for the Gaussian approximations of probability distributions. Special attention is devoted to establishing explicit connections with the classic method of moments: in particular, we use interpolation techniques in order to deduce some new estimates for the moments of random variables belonging to a fixed Wiener chaos. As an illustration, a class of central limit theorems associated with the quadratic variation of a fractional Brownian motion is studied in detail.

Mots clés: Fractional Brownian motion; Isonormal Gaussian processes; Malliavin calculus; Multiple integrals; Stein's method; Central limit theorems

Domaines: Probabilités [math.PR]

Ivan Nourdin, Giovanni Peccati. Stein's method meets Malliavin calculus: a short survey with new estimates. 2009. ⟨hal-00398006v2⟩