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Subexponential loss rate asymptotics for Lévy processes

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  • Institut for Matematiske Fag
  • Center for Bioinformatik (BiRC)
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.
OriginalsprogEngelsk
TidsskriftMathematical Methods of Operations Research
Vol/bind73
Nummer1
Sider (fra-til)91-108
Antal sider18
ISSN1432-2994
DOI
StatusUdgivet - 2011

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