Mixture results for extremal behaviour of strongly dependent nonstationary Gaussian sequences

Abstract

Abstract Let {X n } be a nonstationary Gaussian sequence. In this work we introduce a condition onr ij =Cor(X i ,X j ),i,j=1 that models a strong dependence struture. We prove that the limit of the point process of exceedances is a Cox process i.c. a point process whose distribution is a mixture of distributions of simple Poisson processes, regulated by a standard normal law. Moreover, we study the joint limit distribution of the maxima and minima, under linear normalization, and we again find a doubly stochastic behaviour.