Maxima of independent, non-identically distributed Gaussian vectors

Sebastian Engelke, Zakhar Kabluchko, Martin Schlather
2015 Bernoulli  
Let X_i,n,n∈N,1≤ i≤ n, be a triangular array of independent R^d-valued Gaussian random vectors with correlation matrices Σ_i,n. We give necessary conditions under which the row-wise maxima converge to some max-stable distribution which generalizes the class of Hüsler-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
more » ... s 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 ψ(√(γ(h))),h∈R^d, where ψ is a completely monotone function and γ is an arbitrary variogram.
doi:10.3150/13-bej560 fatcat:dnrs54ww4nautaagzewevqgera