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

TY - UNPB

T1 - Tail asymptotics for the supremum of an infinitely divisible field with convolution equivalent Lévy measure

AU - Rønn-Nielsen, Anders

AU - Jensen, Eva B. Vedel

PY - 2014

Y1 - 2014

N2 - We consider a continuous, infinitely divisible random field in Rd given as anintegral of a kernel function with respect to a Lévy basis with convolutionequivalent Lévy measure. For a large class of such random fields we computethe asymptotic probability that the supremum of the field exceeds the level xas x ! 1. Our main result is that the asymptotic probability is equivalent tothe right tail of the underlying Lévy measure.

AB - We consider a continuous, infinitely divisible random field in Rd given as anintegral of a kernel function with respect to a Lévy basis with convolutionequivalent Lévy measure. For a large class of such random fields we computethe asymptotic probability that the supremum of the field exceeds the level xas x ! 1. Our main result is that the asymptotic probability is equivalent tothe right tail of the underlying Lévy measure.

M3 - Working paper

T3 - CSGB Research Reports

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

PB - Aarhus University

ER -