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January 2003 The maximum on a random time interval of a random walk with long-tailed increments and negative drift
Serguei Foss, Stan Zachary
Ann. Appl. Probab. 13(1): 37-53 (January 2003). DOI: 10.1214/aoap/1042765662

Abstract

We study the asymptotics for the maximum on a random time interval of a random walk with a long-tailed distribution of its increments and negative drift. We extend to a general stopping time a result by Asmussen, simplify its proof and give some converses.

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Serguei Foss. Stan Zachary. "The maximum on a random time interval of a random walk with long-tailed increments and negative drift." Ann. Appl. Probab. 13 (1) 37 - 53, January 2003. https://doi.org/10.1214/aoap/1042765662

Information

Published: January 2003
First available in Project Euclid: 16 January 2003

zbMATH: 1045.60039
MathSciNet: MR1951993
Digital Object Identifier: 10.1214/aoap/1042765662

Subjects:
Primary: 60G70
Secondary: 60K25 , 60K30

Keywords: long-tailed distribution , ruin probability , subexponential distribution

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.13 • No. 1 • January 2003
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