Quantitative stable limit theorems on the Wiener space

Ivan Nourdin (1) , David Nualart (2) , Giovanni Peccati (3)

1 IECL - Institut Élie Cartan de Lorraine
2 Department of Mathematics [Lawrence, Kansas]
3 FSTC - Faculté des Sciences, de la Technologie et de la Communication

We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multi-dimensional mixture of Gaussian distributions. Our findings refine and generalize previous works by Nourdin and Nualart (2010) and Harnett and Nualart (2012), and provide a substantial contribution to a recent line of research, focussing on limit theorems on the Wiener space, obtained by means of the Malliavin calculus of variations. Applications are given to quadratic functionals and weighted quadratic variations of a fractional Brownian motion.

Mots clés: Malliavin calculus; Stable convergence; fractional Brownian motion

Domaines: Probabilités [math.PR]

Ivan Nourdin, David Nualart, Giovanni Peccati. Quantitative stable limit theorems on the Wiener space. Annals of Probability, 2016, 44 (1), pp.1-41. ⟨10.1214/14-AOP965⟩. ⟨hal-00823380⟩