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February 2002 Tail Probabilities of Subadditive Functionals of Lévy Processes
Michael Braverman, Thomas Mikosch, Gennady Samorodnitsky
Ann. Appl. Probab. 12(1): 69-100 (February 2002). DOI: 10.1214/aoap/1015961156

Abstract

We study the tail behavior of the distribution of certain subadditive functionals acting on the sample paths of Lévy processes. The functionals we consider have, roughly speaking, the following property: only the points of the process that lie above a certain curve contribute to the value of the functional. Our assumptions will make sure that the process ends up eventually below the curve. Our results apply to ruin probabilities, distributions of sojourn times over curves, last hitting times and other functionals.

Citation

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Michael Braverman. Thomas Mikosch. Gennady Samorodnitsky. "Tail Probabilities of Subadditive Functionals of Lévy Processes." Ann. Appl. Probab. 12 (1) 69 - 100, February 2002. https://doi.org/10.1214/aoap/1015961156

Information

Published: February 2002
First available in Project Euclid: 12 March 2002

zbMATH: 1035.60045
MathSciNet: MR1890057
Digital Object Identifier: 10.1214/aoap/1015961156

Subjects:
Primary: 60E07
Secondary: 60G10 , 60K30

Keywords: heavy tails , last hitting time , Lévy process , negative drift , risk , ruin probability , sojourn time , subadditive functional , supremum

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.12 • No. 1 • February 2002
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