Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Multivariate normal approximation using Stein’s method and Malliavin calculus

Ivan Nourdin, Giovanni Peccati, and Anthony Réveillac

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We combine Stein’s method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of Gaussian fields. Among several examples, we provide an application to a functional version of the Breuer–Major CLT for fields subordinated to a fractional Brownian motion.


Nous expliquons comment combiner la méthode de Stein avec les outils du calcul de Malliavin pour majorer, de manière explicite, la distance de Wasserstein entre une fonctionnelle d’un champs gaussien donnée et son approximation normale multidimensionnelle. Entre autres exemples, nous associons des bornes à la version fonctionnelle du théorème de la limite centrale de Breuer–Major, dans le cas du mouvement brownien fractionnaire.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 46, Number 1 (2010), 45-58.

First available in Project Euclid: 1 March 2010

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 60G15: Gaussian processes 60H07: Stochastic calculus of variations and the Malliavin calculus

Breuer–Major CLT fractional Brownian motion Gaussian processes Malliavin calculus Normal approximation Stein’s method Wasserstein distance


Nourdin, Ivan; Peccati, Giovanni; Réveillac, Anthony. Multivariate normal approximation using Stein’s method and Malliavin calculus. Ann. Inst. H. Poincaré Probab. Statist. 46 (2010), no. 1, 45--58. doi:10.1214/08-AIHP308.

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