The maximum on a random time interval of a random walk with long-tailed increments and negative drift

Authors
Foss, Serguei Zachary, Stan
Citation
Foss, Serguei et Zachary, Stan, The maximum on a random time interval of a random walk with long-tailed increments and negative drift, Annals of applied probability , 13(1), 2003, pp. 37-53
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
13
Issue
1
Year of publication
2003
Pages
37 - 53
Database
ACNP
SICI code
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.