EQUIVALENT REPRESENTATIONS OF MAX-STABLE PROCESSES VIA l(p)-NORMS

作者：Oesting Marco^*

来源：Journal of Applied Probability, 2018, 55(1): 54-68.

DOI：10.1017/jpr.2018.5

• Extreme value theory
• Reich-Shaby model
• spectral representation
• stable tail dependence function

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 l(p)-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 l(p)-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.

• 出版日期2018-3