Multivariate normal approximation using Stein's method and Malliavin calculus
Annales de l'I.H.P. Probabilités et statistiques, Volume 46 (2010) no. 1, pp. 45-58.

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.

DOI: 10.1214/08-AIHP308
Classification: 60F05,  60G15,  60H07
Keywords: Breuer-Major CLT, fractional brownian motion, gaussian processes, Malliavin calculus, normal approximation, Stein's method, Wasserstein distance
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     title = {Multivariate normal approximation using {Stein's} method and {Malliavin} calculus},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
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     publisher = {Gauthier-Villars},
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Nourdin, Ivan; Peccati, Giovanni; Réveillac, Anthony. Multivariate normal approximation using Stein's method and Malliavin calculus. Annales de l'I.H.P. Probabilités et statistiques, Volume 46 (2010) no. 1, pp. 45-58. doi : 10.1214/08-AIHP308. http://archive.numdam.org/articles/10.1214/08-AIHP308/

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