Tail Asymptotics for the Supremum of an Infinitely Divisible Field with Convolution Equivalent Lévy Measure

Anders  Rønn-Nielsen; Eva B. Vedel Jensen

doi:10.1017/jpr.2015.22

Tail Asymptotics for the Supremum of an Infinitely Divisible Field with Convolution Equivalent Lévy Measure

Anders Rønn-Nielsen, Eva B. Vedel Jensen

Research output: Contribution to journal › Journal article › Research › peer-review

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

Original language	English
Journal	Journal of Applied Probability
Volume	53
Issue number	1
Pages (from-to)	244–261
Number of pages	18
ISSN	0021-9002
DOIs	https://doi.org/10.1017/jpr.2015.22
Publication status	Published - 2016
Externally published	Yes

Keywords

Asymptotic supremum
Convolution equivalence
Infinite divisibility
Lévybased modelling

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Cite this

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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 an integral of a kernel function with respect to a L{\'e}vy basis with convolution equivalent L{\'e}vy measure. For a large class of such random fields we compute the asymptotic probability that thesupremum 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 L{\'e}vy measure.",

keywords = "Asymptotic supremum, Convolution equivalence, Infinite divisibility, L{\'e}vybased modelling, Asymptotic supremum, Convolution equivalence, Infinite divisibility, L{\'e}vybased modelling",

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doi = "10.1017/jpr.2015.22",

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volume = "53",

pages = "244–261",

journal = "Journal of Applied Probability",

issn = "0021-9002",

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AU - Rønn-Nielsen, Anders

AU - Jensen, Eva B. Vedel

PY - 2016

Y1 - 2016

N2 - 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 thesupremum 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 Lévy measure.

AB - 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 thesupremum 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 Lévy measure.

KW - Asymptotic supremum

KW - Convolution equivalence

KW - Infinite divisibility

KW - Lévybased modelling

KW - Asymptotic supremum

KW - Convolution equivalence

KW - Infinite divisibility

KW - Lévybased modelling

U2 - 10.1017/jpr.2015.22

DO - 10.1017/jpr.2015.22

M3 - Journal article

SN - 0021-9002

VL - 53

SP - 244

EP - 261

JO - Journal of Applied Probability

JF - Journal of Applied Probability

IS - 1

ER -