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

Sergey Foss; Stan Zachary

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arXiv · 1303.4432

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

Sergey Foss·Stan Zachary

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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 (1998), simplify its proof, and give some converses.

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Sergey Foss, Stan Zachary. 2013-03-18. The maximum on a random time interval of a random walk with long-tailed increments and negative drift. https://arxiv.org/abs/1303.4432

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