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

Anders Rønn-Nielsen, Eva B. Vedel Jensen

Research output: Contribution to journalJournal articleResearchpeer-review

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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
ISSN0021-9002
DOIs
Publication statusPublished - 2017

Keywords

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

Cite this

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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 L{\'e}vy basis with convolution equivalent L{\'e}vy 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 L{\'e}vy measure.",
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Excursion Sets of Infinitely Divisble Random Fields with Convolution Equivalent Lévy Measure. / Rønn-Nielsen, Anders ; Jensen, Eva B. Vedel.

In: Journal of Applied Probability, Vol. 54, No. 3, 2017, p. 833-851.

Research output: Contribution to journalJournal articleResearchpeer-review

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AB - 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.

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