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Extremal [formula omitted]processes: Elliptical domain of attraction and a spectral representation

Authors
Journal
Journal of Multivariate Analysis
0047-259X
Publisher
Elsevier
Volume
122
Identifiers
DOI: 10.1016/j.jmva.2013.08.008
Keywords
  • Elliptical Distribution
  • Extremal [Formula Omitted]Process
  • Max-Stable Process
  • Spectral Construction

Abstract

Abstract The extremal t process was proposed in the literature for modeling spatial extremes within a copula framework based on the extreme value limit of elliptical t distributions (Davison et al. (2012) [5]). A major drawback of this max-stable model was the lack of a spectral representation such that for instance direct simulation was infeasible. The main contribution of this note is to propose such a spectral construction for the extremal t process. Interestingly, the extremal Gaussian process introduced by Schlather (2002) [22] appears as a special case. We further highlight the role of the extremal t process as the maximum attractor for processes with finite-dimensional elliptical distributions. All results naturally also hold within the multivariate domain.

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