Journal of Applied Probability
- J. Appl. Probab.
- Volume 53, Number 1 (2016), 244-261.
Tail asymptotics for the supremum of an infinitely divisible field with convolution equivalent Lévy measure
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.
J. Appl. Probab., Volume 53, Number 1 (2016), 244-261.
First available in Project Euclid: 8 March 2016
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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. https://projecteuclid.org/euclid.jap/1457470572