Multivariate max-stable processes and homogeneous functionals

Abstract

Multivariate max-stable processes are important for both theoretical investigations and various statistical applications motivated by the fact that these are limiting processes, for instance of stationary multivariate regularly varying time series, (Dombry et al., 2018). In this contribution we explore the relation between homogeneous functionals and multivariate max-stable processes and discuss the connections between multivariate max-stable process and zonoid/max-zonoid equivalence. We illustrate our results considering Brown–Resnick and Smith processes.