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

Annals of Applied Probability (2003) 13(1) 37-53
DOI: 10.1214/aoap/1042765662
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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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Foss, S., & Zachary, S. (2003). The maximum on a random time interval of a random walk with long-tailed increments and negative drift. Annals of Applied Probability, 13(1), 37–53. https://doi.org/10.1214/aoap/1042765662

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