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

Anders Rønn-Nielsen
(Department of Mathematical Sciences, University of Copenhagen)
Torsdag, 23 oktober, 2014, at 13:15-14:00, in Koll. D (1531-211)

A continuous, infinitely divisible d-dimensional random field given as an integral of a kernel function with respect to a Lévy basis with convolution equivalent Lévy measure is considered. For a large class of such random fields the asymptotic probability that the supremum of the field exceeds the level x is computed as x tends to infinity. The main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure. Furthermore the asymptotic behaviour of the probability that an excursion set contains e.g. a ball of a given size is studied. Also this probability is asymptotically described by the right tail of the Lévy measure.

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