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

  • Anders Rønn-Nielsen and Eva B. Vedel Jensen (a1)

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.

Corresponding author
*Department of Mathematical Sciences, University of Copenhagen, Universitetspark 5, 2100 Copenhagen Ø, Denmark. Email address:
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