Article: article from journal or magazin.
Limit laws for extremes of dependent stationary Gaussian arrays
Statistics & Probability Letters
In this paper we show that the componentwise maxima of weakly dependent bivariate stationary Gaussian triangular arrays converge in distribution after appropriate normalization to Husler-Reiss distribution. Under a strong dependence assumption, we prove that the limit distribution of the maxima is a mixture of a bivariate Gaussian distribution and Husler-Reiss distribution. An important new finding of our paper is that the componentwise maxima and componentwise minima remain asymptotically independent even in the settings of Husler and Reiss (1989) allowing further for weak dependence. Further we derive an almost sure limit theorem under the Berman condition for the components of the triangular array.
Husler-Reiss distribution, Brown-Resnick copula, Gumbel max-domain of attraction, Berman condition, Almost sure limit theorem
Web of science
Last modification date