Subexponential loss rate asymptotics for Lévy processes

Lars Andersen ()

Mathematical Methods of Operations Research, 2011, vol. 73, issue 1, 108 pages

Abstract: We consider a Lévy process reflected in barriers at 0 and K > 0. The loss rate is the mean of the local time at K at time 1 when the process is started in stationarity, and is a natural continuous-time analogue of the stationary expected loss rate for a reflected random walk. We derive asymptotics for the loss rate when K tends to infinity, when the mean of the Lévy process is negative and the positive jumps are subexponential. In the course of this derivation, we achieve a formula, which is a generalization of the celebrated Pollaczeck-Khinchine formula. Copyright Springer-Verlag 2011

Keywords: Finite buffer; Heavy tails; Lévy process; Local times; Loss rate; Pollaczeck-Khinchine formula; Subexponential distributions (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00186-010-0335-0

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