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.
Citation
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
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