Tail asymptotics for exponential functionals of Lévy processes: The convolution equivalent case

Víctor Rivero

Annales de l'I.H.P. Probabilités et statistiques (2012)

  • Volume: 48, Issue: 4, page 1081-1102
  • ISSN: 0246-0203

Abstract

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We determine the rate of decrease of the right tail distribution of the exponential functional of a Lévy process with a convolution equivalent Lévy measure. Our main result establishes that it decreases as the right tail of the image under the exponential function of the Lévy measure of the underlying Lévy process. The method of proof relies on fluctuation theory of Lévy processes and an explicit pathwise representation of the exponential functional as the exponential functional of a bivariate subordinator. Our techniques allow us to establish analogous results under the excursion measure of the underlying Lévy process reflected in its past infimum.

How to cite

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Rivero, Víctor. "Tail asymptotics for exponential functionals of Lévy processes: The convolution equivalent case." Annales de l'I.H.P. Probabilités et statistiques 48.4 (2012): 1081-1102. <http://eudml.org/doc/271989>.

@article{Rivero2012,
abstract = {We determine the rate of decrease of the right tail distribution of the exponential functional of a Lévy process with a convolution equivalent Lévy measure. Our main result establishes that it decreases as the right tail of the image under the exponential function of the Lévy measure of the underlying Lévy process. The method of proof relies on fluctuation theory of Lévy processes and an explicit pathwise representation of the exponential functional as the exponential functional of a bivariate subordinator. Our techniques allow us to establish analogous results under the excursion measure of the underlying Lévy process reflected in its past infimum.},
author = {Rivero, Víctor},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {convolution equivalent distributions; exponential functionals of Lévy processes; fluctuation theory of Lévy processes; exponential functionals of Levy processes; fluctuation theory of Levy processes},
language = {eng},
number = {4},
pages = {1081-1102},
publisher = {Gauthier-Villars},
title = {Tail asymptotics for exponential functionals of Lévy processes: The convolution equivalent case},
url = {http://eudml.org/doc/271989},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Rivero, Víctor
TI - Tail asymptotics for exponential functionals of Lévy processes: The convolution equivalent case
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2012
PB - Gauthier-Villars
VL - 48
IS - 4
SP - 1081
EP - 1102
AB - We determine the rate of decrease of the right tail distribution of the exponential functional of a Lévy process with a convolution equivalent Lévy measure. Our main result establishes that it decreases as the right tail of the image under the exponential function of the Lévy measure of the underlying Lévy process. The method of proof relies on fluctuation theory of Lévy processes and an explicit pathwise representation of the exponential functional as the exponential functional of a bivariate subordinator. Our techniques allow us to establish analogous results under the excursion measure of the underlying Lévy process reflected in its past infimum.
LA - eng
KW - convolution equivalent distributions; exponential functionals of Lévy processes; fluctuation theory of Lévy processes; exponential functionals of Levy processes; fluctuation theory of Levy processes
UR - http://eudml.org/doc/271989
ER -

References

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