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

Anders Rønn-Nielsen; Eva B. Vedel Jensen

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

Anders Rønn-Nielsen, Eva B. Vedel Jensen

Institut for Matematiske Fag

Abstract

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 ! 1. Our main result is that the asymptotic probability is equivalent to
the right tail of the underlying Lévy measure.

Originalsprog	Engelsk
Udgiver	Aarhus University
Status	Udgivet - 2014

Navn	CSGB Research Reports
Nummer	9
Vol/bind	2014

Citationsformater

@techreport{f028ca677b9740f68a54f9305b3cb672,

title = "Tail asymptotics for the supremum of an infinitely divisible field with convolution equivalent L{\'e}vy measure",

abstract = "We consider a continuous, infinitely divisible random field in Rd given as anintegral of a kernel function with respect to a L{\'e}vy basis with convolutionequivalent L{\'e}vy 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 L{\'e}vy measure.",

author = "Anders R{\o}nn-Nielsen and Jensen, {Eva B. Vedel}",

year = "2014",

language = "English",

series = "CSGB Research Reports",

number = "9",

publisher = "Aarhus University",

type = "WorkingPaper",

institution = "Aarhus University",

}

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 -

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

Abstract

Fingeraftryk

Citationsformater