Suprema of compound Poisson processes with light tails

Michael Braverman

doi:10.1016/S0304-4149(00)00039-9

Suprema of compound Poisson processes with light tails

Michael Braverman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

It is known that if the Lévy measure of a Lévy process X(t), 0≤t≤1, is "heavy tailed", then the right tails of sup_0≤t≤1X(t) and X(1) are of the same rate of decay. One of the results of this note is a description of a class of compound Poisson processes with negative drift and "light" tails (which is a subclass of Lévy processes) such that these tails are incomparable.

Original language	English
Pages (from-to)	145-156
Number of pages	12
Journal	Stochastic Processes and their Applications
Volume	90
Issue number	1
DOIs	https://doi.org/10.1016/S0304-4149(00)00039-9
State	Published - 1 Jan 2000

Keywords

Compound poisson process
Lévy process
Tail behavior

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/S0304-4149(00)00039-9

Cite this

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title = "Suprema of compound Poisson processes with light tails",

abstract = "It is known that if the L{\'e}vy measure of a L{\'e}vy process X(t), 0≤t≤1, is {"}heavy tailed{"}, then the right tails of sup0≤t≤1X(t) and X(1) are of the same rate of decay. One of the results of this note is a description of a class of compound Poisson processes with negative drift and {"}light{"} tails (which is a subclass of L{\'e}vy processes) such that these tails are incomparable.",

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N2 - It is known that if the Lévy measure of a Lévy process X(t), 0≤t≤1, is "heavy tailed", then the right tails of sup0≤t≤1X(t) and X(1) are of the same rate of decay. One of the results of this note is a description of a class of compound Poisson processes with negative drift and "light" tails (which is a subclass of Lévy processes) such that these tails are incomparable.

AB - It is known that if the Lévy measure of a Lévy process X(t), 0≤t≤1, is "heavy tailed", then the right tails of sup0≤t≤1X(t) and X(1) are of the same rate of decay. One of the results of this note is a description of a class of compound Poisson processes with negative drift and "light" tails (which is a subclass of Lévy processes) such that these tails are incomparable.

KW - Compound poisson process

KW - Lévy process

KW - Tail behavior

UR - https://www.scopus.com/pages/publications/0346675062

U2 - 10.1016/S0304-4149(00)00039-9

DO - 10.1016/S0304-4149(00)00039-9

M3 - Article

AN - SCOPUS:0346675062

SN - 0304-4149

VL - 90

SP - 145

EP - 156

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 1

ER -

Suprema of compound Poisson processes with light tails

Abstract

Keywords

ASJC Scopus subject areas

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