Max-stable processes and the functional D-norm revisited

TL;DR

This paper revisits max-stable processes and the functional D-norm, providing new characterizations and exploring convergence rates and differentiability in distribution within the framework of extreme value theory.

Contribution

It offers a decomposition-based characterization of max-domain of attraction for max-stable processes and examines convergence rates and differentiability properties.

Findings

Processes with polynomial convergence rates are characterized.

Decomposition into margins and copula process is key.

Differentiability in distribution of max-stable processes is analyzed.

Abstract

Aulbach et al. (2013) introduced a max-domain of attraction approach for extreme value theory in C[0,1] based on functional distribution functions, which is more general than the approach based on weak convergence in de Haan and Lin (2001). We characterize this new approach by decomposing a process into its univariate margins and its copula process. In particular, those processes with a polynomial rate of convergence towards a max-stable process are considered. Furthermore we investigate the concept of differentiability in distribution of a max-stable processes.