Extremes of Lévy-driven Spatial Random Fields with Regularly Varying Lévy Measure

Anders Rønn-Nielsen, Mads Stehr*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


We consider an infinitely divisible random field indexed by given as an integral of a kernel function with respect to a Lévy basis with a Lévy measure having a regularly varying right tail. First we show that the tail of its supremum over any bounded set is asymptotically equivalent to the right tail of the Lévy measure times the integral of the kernel. Secondly, when observing the field over an appropriately increasing sequence of continuous index sets, we obtain an extreme value theorem stating that the running supremum converges in distribution to the Fréchet distribution.
Original languageEnglish
JournalStochastic Processes and Their Applications
Pages (from-to)19-49
Number of pages31
Publication statusPublished - Aug 2022


  • Extreme value theory
  • Lévy-based modeling
  • Regular variation
  • Geometric probability
  • Random fields

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