Journal of Applied Probability

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

Anders Rønn-Nielsen and Eva B. Vedel Jensen

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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.

Article information

J. Appl. Probab., Volume 53, Number 1 (2016), 244-261.

First available in Project Euclid: 8 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G60: Random fields
Secondary: 60E07: Infinitely divisible distributions; stable distributions 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Asymptotic supremum convolution equivalence infinite divisibility Lévy-based modelling


Rønn-Nielsen, Anders; Jensen, Eva B. Vedel. Tail asymptotics for the supremum of an infinitely divisible field with convolution equivalent Lévy measure. J. Appl. Probab. 53 (2016), no. 1, 244--261.

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