Asymptotics of the Norm of Elliptical Random Vectors

In this paper we consider elliptical random vectors X in R^d,d>1 with stochastic representation A R U where R is a positive random radius independent of the random vector U which is uniformly distributed on the unit sphere of R^d and A is a given matrix. The main result of this paper is an asymptotic expansion of the tail probability of the norm of X derived under the assumption that R has distribution function is in the Gumbel or the Weibull max-domain of attraction.