Multivariate normal approximation using Stein’s method and Malliavin calculus

Ivan Nourdin; Giovanni Peccati; Anthony Réveillac

Annales de l'I.H.P. Probabilités et statistiques (2010)

  • Volume: 46, Issue: 1, page 45-58
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Nourdin, Ivan, Peccati, Giovanni, and Réveillac, Anthony. "Multivariate normal approximation using Stein’s method and Malliavin calculus." Annales de l'I.H.P. Probabilités et statistiques 46.1 (2010): 45-58. <http://eudml.org/doc/241128>.

@article{Nourdin2010,
abstract = {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.},
author = {Nourdin, Ivan, Peccati, Giovanni, Réveillac, Anthony},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Breuer–Major CLT; fractional brownian motion; gaussian processes; Malliavin calculus; normal approximation; Stein’s method; Wasserstein distance; Stein's method},
language = {eng},
number = {1},
pages = {45-58},
publisher = {Gauthier-Villars},
title = {Multivariate normal approximation using Stein’s method and Malliavin calculus},
url = {http://eudml.org/doc/241128},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Nourdin, Ivan
AU - Peccati, Giovanni
AU - Réveillac, Anthony
TI - Multivariate normal approximation using Stein’s method and Malliavin calculus
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2010
PB - Gauthier-Villars
VL - 46
IS - 1
SP - 45
EP - 58
AB - 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.
LA - eng
KW - Breuer–Major CLT; fractional brownian motion; gaussian processes; Malliavin calculus; normal approximation; Stein’s method; Wasserstein distance; Stein's method
UR - http://eudml.org/doc/241128
ER -

References

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