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

Anders Rønn-Nielsen, Eva B. Vedel Jensen

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Abstrakt

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.
OriginalsprogEngelsk
TidsskriftJournal of Applied Probability
Vol/bind53
Udgave nummer1
Sider (fra-til)244–261
Antal sider18
ISSN0021-9002
DOI
StatusUdgivet - 2016
Udgivet eksterntJa

Emneord

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

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