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.
"Tail asymptotics for the supremum of an infinitely divisible field with convolution equivalent Lévy measure." J. Appl. Probab. 53 (1) 244 - 261, March 2016.