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

Anders Rønn-Nielsen, Mads Stehr*

*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer 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.
TidsskriftStochastic Processes and Their Applications
Sider (fra-til)19-49
Antal sider31
StatusUdgivet - aug. 2022


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