Tail Asymptotics of an Infinitely Divisible Space-time Model with Convolution Equivalent Lévy Measure

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Abstract

We consider a space-time random field on given as an integral of a kernel function with respect to a Lévy basis with a convolution equivalent Lévy measure. The field obeys causality in time and is thereby not continuous along the time axis. For a large class of such random fields we study the tail behaviour of certain functionals of the field. It turns out that the tail is asymptotically equivalent to the right tail of the underlying Lévy measure. Particular examples are the asymptotic probability that there is a time point and a rotation of a spatial object with fixed radius, in which the field exceeds the level x, and that there is a time interval and a rotation of a spatial object with fixed radius, in which the average of the field exceeds the level x.
Original languageEnglish
JournalJournal of Applied Probability
Volume58
Issue number1
Pages (from-to)42-67
Number of pages26
ISSN0021-9002
DOIs
Publication statusPublished - Mar 2021

Bibliographical note

Epub ahead of print. Published online: 25. Februar 2021

Keywords

  • Convolution equivalence
  • Infinite divisibility
  • Lévy-based modelling
  • Asymptotic equivalence
  • Sample paths for random fields

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