A Note on Veraverbeke's Theorem

Authors:
Stan Zachary
Affiliations:
Heriot-Watt University, Edinburgh
Venue:
Queueing Systems: Theory and Applications
Year:
2004

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Abstract

We give an elementary probabilistic proof of Veraverbeke's theorem for the asymptotic distribution of the maximum of a random walk with negative drift and heavy-tailed increments. The proof gives insight into the principle that the maximum is in general attained through a single large jump.