Maxima of independent, non-identically distributed Gaussian vectors

摘要

Let X-i,X-n, n is an element of N,1 <= i <= n, be a triangular array of independent R-d-valued Gaussian random vectors with correlation matrices Sigma(i,n). We give necessary conditions under which the row-wise maxima converge to some max-stable distribution which generalizes the class of Husler-Reiss distributions. In the bivariate case, the conditions will also be sufficient. Using these results, new models for bivariate extremes are derived explicitly. Moreover, we define a new class of stationary, max-stable processes as max-mixtures of Brown-Resnick processes. As an application, we show that these processes realize a large set of extremal correlation functions, a natural dependence measure for max-stable processes. This set includes all functions psi (root gamma(h)), h is an element of R-d, where psi is a completely monotone function and gamma is an arbitrary variogram.