Extremes of Lévy-driven spatial random fields with regularly varying Lévy measure

Anders Rønn-Nielsen and Mads Stehr

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 19-49

Abstract: We consider an infinitely divisible random field indexed by Rd, d∈N, given as an integral of a kernel function with respect to a Lévy basis with a Lévy measure having a regularly varying right tail. First we show that the tail of its supremum over any bounded set is asymptotically equivalent to the right tail of the Lévy measure times the integral of the kernel. Secondly, when observing the field over an appropriately increasing sequence of continuous index sets, we obtain an extreme value theorem stating that the running supremum converges in distribution to the Fréchet distribution.

Keywords: Extreme value theory; Lévy-based modeling; Regular variation; Geometric probability; Random fields (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2022.04.007

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