Excursion sets of infinitely divisible random fields with convolution equivalent Lévy measure

TY - UNPB

T1 - Excursion sets of infinitely divisible random fields with convolution equivalent Lévy measure

AU - Rønn-Nielsen, Anders

AU - Jensen, Eva B. Vedel

PY - 2016/8

Y1 - 2016/8

N2 - We consider a continuous, infinitely divisible random field in Rd , d = 1, 2, 3, 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 excursion set at level x contains some rotation of an object with fixed radius as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure

AB - We consider a continuous, infinitely divisible random field in Rd , d = 1, 2, 3, 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 excursion set at level x contains some rotation of an object with fixed radius as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure

M3 - Working paper

T3 - CSGB Research Reports

BT - Excursion sets of infinitely divisible random fields with convolution equivalent Lévy measure

PB - Aarhus University

ER -