Extremes of Subexponential Lévy-driven Random Fields in the Gumbel Domain of Attraction

Mads Stehr*, Anders Rønn-Nielsen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


We consider a spatial Lévy-driven moving average with an underlying Lévy measure having a subexponential right tail, which is also in the maximum domain of attraction of the Gumbel distribution. Assuming that the left tail is not heavier than the right tail, and that the integration kernel satisfies certain regularity conditions, we show that the supremum of the field over any bounded set has a right tail equivalent to that of the Lévy measure. Furthermore, for a very general class of expanding index sets, we show that the running supremum of the field, under a suitable scaling, converges to the Gumbel distribution.
Original languageEnglish
Issue number1
Pages (from-to)79–105
Number of pages27
Publication statusPublished - Mar 2022

Bibliographical note

Published online: 11 September 2021.


  • Extreme value theory
  • Lévy-based modeling
  • Geometric probability
  • Subexponential distributions
  • Random fields

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