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

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