Extremes of asymptotically spherical and elliptical random vectors

In this paper we introduce asymptotically spherical and elliptical random vectors. Based on results of Berman [Berman, M.S., 1992. Sojurns and Extremes of Stochastic Processes. Wadsworth & Brooks/Cole], we study the asymptotic behaviour of the sample extremes for both these new classes of random vectors. Related results for the coefficient of upper tail dependence are further derived.