Asymptotic expansion of Gaussian chaos via probabilistic approach

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ID Serval
serval:BIB_2D3E2C5A2FA5
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Asymptotic expansion of Gaussian chaos via probabilistic approach
Périodique
Extremes
Auteur(s)
Hashorva  E., Korshunov  D., Piterbarg  V.I.
ISSN
1386-1999 (Print)
1572-915X (Electronic)
Statut éditorial
Publié
Date de publication
09/2015
Peer-reviewed
Oui
Volume
18
Numéro
3
Pages
315-347
Langue
anglais
Résumé
For a centered d-dimensional Gaussian random vector xi = (xi(1),..., xi (d) ) and a homogeneous function h : R-d -> R we derive asymptotic expansions for the tail of the Gaussian chaos h(xi) given the function h is sufficiently smooth. Three challenging instances of the Gaussian chaos are the determinant of a Gaussian matrix, the Gaussian orthogonal ensemble and the diameter of random Gaussian clouds. Using a direct probabilistic asymptotic method, we investigate both the asymptotic behaviour of the tail distribution of h(xi) and its density at infinity and then discuss possible extensions for some general xi with polar representation.
Mots-clé
Wiener chaos, Polynomial chaos, Gaussian chaos, Multidimensional normal distribution, Subexponential distribution, Determinant of a random matrix, Gaussian orthogonal ensemble, Diameter of random Gaussian clouds, Max-domain of attraction
Web of science
Création de la notice
23/02/2015 13:07
Dernière modification de la notice
20/08/2019 13:12
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