Minima and maxima of elliptical arrays and spherical processes

Abstract

In this paper, we investigate first the asymptotics of the minima of elliptical triangular arrays. Motivated by the findings of Kabluchko (Extremes 14 (2011) 285-310), we discuss further the asymptotic behaviour of the maxima of elliptical triangular arrays with marginal distribution functions in the Gumbel or Weibull max-domain of attraction. We present an application concerning the asymptotics of the maximum and the minimum of independent spherical processes.

Published in at http://dx.doi.org/10.3150/12-BEJ463 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (3)

• Stationary max-stable fields associated to negative definite functions
• Asymptotics of supremum distribution of a Gaussian process over a Weibullian time
• On Beta-Product Convolutions

Cited by in corpus (6)

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• Efficient simulation of tail probabilities for sums of log-elliptical risks
• Asymptotic behaviors of bivariate Gaussian powered extremes
• Bridging Asymptotic Independence and Dependence in Spatial Extremes Using Gaussian Scale Mixtures
• Maxima and minima of independent and non-identically distributed bivariate Gaussian triangular arrays
• Berman's inequality under random scaling