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1 results

  • Equivalent representations of max-stable processes via ℓp-norms

  • Part of
  • Marco Oesting
  • Journal:
    Journal of Applied Probability / Volume 55 / Issue 1 / March 2018
    Published online by Cambridge University Press:
    28 March 2018, pp. 54-68
    Print publication:
    March 2018

  • While max-stable processes are typically written as pointwise maxima over an infinite number of stochastic processes, in this paper, we consider a family of representations based on ℓp-norms. This family includes both the construction of the Reich–Shaby model and the classical spectral representation by de Haan (1984) as special cases. As the representation of a max-stable process is not unique, we present formulae to switch between different equivalent representations. We further provide a necessary and sufficient condition for the existence of an ℓp-norm-based representation in terms of the stable tail dependence function of a max-stable process. Finally, we discuss several properties of the represented processes such as ergodicity or mixing.