Tail Asymptotics for the Supremum of an Infinitely Divisible Field with Convolution Equivalent Lévy Measure

Anders Rønn-Nielsen, Eva B. Vedel Jensen

Research output: Contribution to journalJournal articleResearchpeer-review


We consider a continuous, infinitely divisible random field in Rd given as an integral of a kernel function with respect to a Lévy basis with convolution equivalent Lévy measure. For a large class of such random fields we compute the asymptotic probability that the
supremum of the field exceeds the level x as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure.
Original languageEnglish
JournalJournal of Applied Probability
Issue number1
Pages (from-to)244–261
Number of pages18
Publication statusPublished - 2016
Externally publishedYes


  • Asymptotic supremum
  • Convolution equivalence
  • Infinite divisibility
  • Lévybased modelling

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