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.
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Zachary, S. A Note on Veraverbeke's Theorem. Queueing Systems 46, 9–14 (2004). https://doi.org/10.1023/B:QUES.0000021155.44510.9f
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DOI: https://doi.org/10.1023/B:QUES.0000021155.44510.9f