The probability of exceeding a high boundary on a random time interval for a heavy-tailed random walk

Authors
Foss, Serguei Palmowski, Zbigniew Zachary, Stan
Citation
Foss, Serguei et al., The probability of exceeding a high boundary on a random time interval for a heavy-tailed random walk, Annals of applied probability , 15(3), 2005, pp. 1936-1957
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
15
Issue
3
Year of publication
2005
Pages
1936 - 1957
Database
ACNP
SICI code
Abstract
We study the asymptotic probability that a random walk with heavy-tailed increments crosses a high boundary on a random time interval. We use new techniques to extend results of Asmussen [Ann. Appl. Probab. 8 (1998) 354.374] to completely general stopping times, uniformity of convergence over all stopping times and a wide class of nonlinear boundaries. We also give some examples and counterexamples.