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

TY - JOUR

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 - 2016/3

Y1 - 2016/3

N2 - We consider a continuous, infinitely divisible random field in Rd given as an integral of a kernel function with respect to a Levy basis with convolution equivalent Levy 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 Levy measure.

AB - We consider a continuous, infinitely divisible random field in Rd given as an integral of a kernel function with respect to a Levy basis with convolution equivalent Levy 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 Levy measure.

U2 - 10.1017/jpr.2015.22

DO - 10.1017/jpr.2015.22

M3 - Journal article

SN - 0021-9002

VL - 53

SP - 244-261.

JO - Journal of Applied Probability

JF - Journal of Applied Probability

IS - 1

ER -