Multivariate Max-Stable Processes and Homogeneous Functionals

TL;DR

This paper explores the relationship between homogeneous functionals and multivariate max-stable processes, highlighting their connections to zonoid equivalence and illustrating with Brown-Resnick and Smith processes.

Contribution

It introduces new insights into the connection between homogeneous functionals and multivariate max-stable processes, including their relation to zonoid equivalence.

Findings

Established links between homogeneous functionals and max-stable processes

Connected multivariate max-stable processes with zonoid and max-zonoid concepts

Illustrated theoretical results with Brown-Resnick and Smith processes

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, [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.