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

Published online by Cambridge University Press:  24 March 2016

Anders Rønn-Nielsen  and
Eva B. Vedel Jensen
Eva B. Vedel Jensen
Affiliation:
Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000 Aarhus C, Denmark. Email address: [email protected]
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Abstract

We consider a continuous, infinitely divisible random field in Rd 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.

Keywords

Asymptotic supremumconvolution equivalenceinfinite divisibilityLévy-based modelling
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 1 , March 2016 , pp. 244 - 261
Copyright
Copyright © Applied Probability Trust 2016 

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