TY - JOUR

T1 - Excursion Sets of Infinitely Divisble Random Fields with Convolution Equivalent Lévy Measure

AU - Rønn-Nielsen, Anders

AU - Jensen, Eva B. Vedel

PY - 2017

Y1 - 2017

N2 - We consider a continuous, infinitely divisible random field in ℝ d , 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 ℝ d , 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.

KW - Convolution equivalence

KW - Excursion set

KW - Infinite divisibility

KW - Lévy-based modelling

KW - Convolution equivalence

KW - Excursion set

KW - Infinite divisibility

KW - Lévy-based modelling

UR - https://sfx-45cbs.hosted.exlibrisgroup.com/45cbs?url_ver=Z39.88-2004&url_ctx_fmt=info:ofi/fmt:kev:mtx:ctx&ctx_enc=info:ofi/enc:UTF-8&ctx_ver=Z39.88-2004&rfr_id=info:sid/sfxit.com:azlist&sfx.ignore_date_threshold=1&rft.object_id=954921347249

U2 - 10.1017/jpr.2017.37

DO - 10.1017/jpr.2017.37

M3 - Journal article

VL - 54

SP - 833

EP - 851

JO - Journal of Applied Probability

JF - Journal of Applied Probability

SN - 0021-9002

IS - 3

ER -