Tail asymptotics for the supremum of an infinitely divisible field with convolution equivalent Lévy measure

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

  • Anders Rønn-Nielsen
  • Eva B. Vedel Jensen
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.
ISSN0021-9002
DOI
StatusUdgivet - 2016

ID: 137321051