Extremes

, Volume 18, Issue 2, pp 191–212 | Cite as

Max-stable processes and the functional D-norm revisited

  • Stefan Aulbach
  • Michael Falk
  • Martin Hofmann
  • Maximilian Zott
Article

Abstract

Aulbach et al. (Extremes 16, 255283, 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 (Ann. Probab. 29, 467483, 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.

Keywords

Max-stable process D-norm Functional max-domain of attraction Copula process Generalized Pareto process δ-neighborhood of generalized Pareto process Derivative of D-norm Distributional differentiability 

AMS 2000 Subject Classifications

60G70 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Stefan Aulbach
    • 1
  • Michael Falk
    • 1
  • Martin Hofmann
    • 1
  • Maximilian Zott
    • 1
  1. 1.Institute of MathematicsUniversity of WürzburgWürzburgGermany

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