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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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