On the regular variation of elliptical random vectors

被引：7

作者：

Hashorva, Enkelejd

机构：

[1] Univ Bern, Dept Math Stat & Actuarial Sci, CH-3012 Bern, Switzerland

[2] Allianz Suisse Insurance Co, CH-3001 Bern, Switzerland

来源：

STATISTICS & PROBABILITY LETTERS | 2006年 / 76卷 / 14期

关键词：

regularly varying vectors; elliptical random vectors; Berman process; Sojourn limit theorem; asymptotics of supremum; coefficient of upper tail dependence;

D O I：

10.1016/j.spl.2006.02.014

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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. (C) 2006 Elsevier B.V. All rights reserved.

引用

页码：1427 / 1434

页数：8

共 19 条

[11]

HASHORVA E, 2004, EXTREMES CONDITIONAL

[12] Multivariate extremes, aggregation and dependence in elliptical distributions [J].