# Excursion sets of infinitely divisible random fields with convolution equivalent Lévy measure

By Anders Rønn-Nielsen and Eva B. Vedel Jensen
CSGB Research Reports
No. 11, August 2016
Abstract:

We consider a continuous, infinitely divisible random field in $$\mathbb{R}^d$$, $$d=1,2,3$$, 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 excursion set at level $$x$$ contains some rotation of an object with fixed radius as $$x\to\infty$$. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure.

Keywords: convolution equivalence; excursion set; infinite divisibility; Lévy-based modelling

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