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

Research paper by Serguei Foss, Stan Zachary

Indexed on: 18 Mar '13Published on: 18 Mar '13Published in: Mathematics - Probability



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.