Max-stable processes and the functional D-norm revisited

Stefan Aulbach, Michael Falk, Martin Hofmann, Maximilian Zott

Published 2013-03-11, updated 2014-12-11Version 4

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.