Excursion Sets of Infinitely Divisble Random Fields with Convolution Equivalent Lévy Measure

Anders Rønn-Nielsen, Eva B. Vedel Jensen

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Abstract

We consider a continuous, infinitely divisible random field in ℝ d , d = 1, 2, 3, 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 excursion set at level x contains some rotation of an object with fixed radius 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
Volume54
Issue number3
Pages (from-to)833-851
Number of pages19
ISSN0021-9002
DOIs
Publication statusPublished - 2017

Keywords

  • Convolution equivalence
  • Excursion set
  • Infinite divisibility
  • Lévy-based modelling

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