  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.
