Annals of Applied Probability

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

Serguei Foss and Stan Zachary

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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.

Article information

Ann. Appl. Probab., Volume 13, Number 1 (2003), 37-53.

First available in Project Euclid: 16 January 2003

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Zentralblatt MATH identifier

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx] 60K25: Queueing theory [See also 68M20, 90B22]

Ruin probability long-tailed distribution subexponential distribution


Foss, Serguei; Zachary, Stan. The maximum on a random time interval of a random walk with long-tailed increments and negative drift. Ann. Appl. Probab. 13 (2003), no. 1, 37--53. doi:10.1214/aoap/1042765662.

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