On the regular variation of elliptical random vectors

Details

Serval ID
serval:BIB_7B752384E958
Type
Article: article from journal or magazin.
Collection
Publications
Title
On the regular variation of elliptical random vectors
Journal
Statistics & Probability Letters
Author(s)
Hashorva E.
ISSN
0167-7152
Publication state
Published
Issued date
2006
Peer-reviewed
Oui
Volume
76
Number
14
Pages
1427-1434
Language
english
Abstract
Let S = (S-1,...,S-d)(T), d >= 2 be a spherical random vector in R-d and let X = A(inverted perpendicular)S be an elliptical random vector with A is an element of R-dxd a non-singular matrix. Berman (1992. Sojourns and Extremes of Stochastic Processes. Wadsworth & Brooks/ Cole) proved that if the random radius R-d = (Sigma(d)(i=1) S-i(2))(1/2) regularly varying with index alpha > 0 then S and S-i, 1 <= i <= d are regularly varying with index alpha. In this paper we derive several new equivalent conditions for the regular variation of X. As a by-product we obtain two asymptotic results concerning the sojourn and supremum of Berman processes.
Keywords
Regularly varying vectors, Elliptical random vectors, Berman process, Sojourn limit theorem, Asymptotics of supremum, Coefficient of upper tail dependence
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Create date
03/09/2010 10:42
Last modification date
20/08/2019 14:37
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