Asymptotic expansion of Gaussian chaos via probabilistic approach
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State: Public
Version: author
License: Not specified
Serval ID
serval:BIB_2D3E2C5A2FA5
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Asymptotic expansion of Gaussian chaos via probabilistic approach
Journal
Extremes
ISSN
1386-1999 (Print)
1572-915X (Electronic)
1572-915X (Electronic)
Publication state
Published
Issued date
09/2015
Peer-reviewed
Oui
Volume
18
Number
3
Pages
315-347
Language
english
Abstract
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.
Keywords
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
Create date
23/02/2015 13:07
Last modification date
20/08/2019 13:12