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

2016; Cambridge University Press; Volume: 53; Issue: 1 Linguagem: Inglês

10.1017/jpr.2015.22

1475-6072

Anders Rønn-Nielsen, Eva B. Vedel Jensen,

Stochastic processes and statistical mechanics

Abstract We consider a continuous, infinitely divisible random field in R d 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 supremum of the field exceeds the level x as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure.