  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, [1]. 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.
