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August 2006 Tail asymptotics for the maximum of perturbed random walk
Victor F. Araman, Peter W. Glynn
Ann. Appl. Probab. 16(3): 1411-1431 (August 2006). DOI: 10.1214/105051606000000268

Abstract

Consider a random walk S=(Sn:n≥0) that is “perturbed” by a stationary sequence (ξn:n≥0) to produce the process (Sn+ξn:n≥0). This paper is concerned with computing the distribution of the all-time maximum M=max {Sk+ξk:k≥0} of perturbed random walk with a negative drift. Such a maximum arises in several different applications settings, including production systems, communications networks and insurance risk. Our main results describe asymptotics for ℙ(M>x) as x→∞. The tail asymptotics depend greatly on whether the ξn’s are light-tailed or heavy-tailed. In the light-tailed setting, the tail asymptotic is closely related to the Cramér–Lundberg asymptotic for standard random walk.

Citation

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Victor F. Araman. Peter W. Glynn. "Tail asymptotics for the maximum of perturbed random walk." Ann. Appl. Probab. 16 (3) 1411 - 1431, August 2006. https://doi.org/10.1214/105051606000000268

Information

Published: August 2006
First available in Project Euclid: 2 October 2006

zbMATH: 1118.60073
MathSciNet: MR2260068
Digital Object Identifier: 10.1214/105051606000000268

Subjects:
Primary: 60F17, 60K25, 68M20, 90F35

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.16 • No. 3 • August 2006
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