On the multivariate Husler-Reiss distribution attracting the maxima of elliptical triangular arrays

Let (X-ln((j)), ..., X-dn((j))), n >= 1, 1 <= j <= n, be a triangular array of independent elliptical random vectors in R-d, d >= 2. In this paper we investigate the asymptotic behaviour of the multivariate maxima of this triangular array. Generalising previous results for the bivariate set-up, we show that the normalised maxima of this elliptical triangular array is attracted by the multivariate Husler-Reiss distribution function provided that the components of the triangular array become asymptotically dependent with a specific rate, and further the random radius pertaining to the elliptical random vectors is in the Gumbel max-domain of attraction. (c) 2006 Elsevier B.V. All rights reserved.