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Subexponential loss rate asymptotics for Lévy processes

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  • Lars Andersen

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

Suggested Citation

  • Lars Andersen, 2011. "Subexponential loss rate asymptotics for Lévy processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(1), pages 91-108, February.
    • Handle: RePEc:spr:mathme:v:73:y:2011:i:1:p:91-108
    DOI: 10.1007/s00186-010-0335-0
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    References listed on IDEAS

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    1. Maulik, Krishanu & Zwart, Bert, 2006. "Tail asymptotics for exponential functionals of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 156-177, February.
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    Cited by:

    1. Xindan Li & Dan Tang & Yongjin Wang & Xuewei Yang, 2014. "Optimal processing rate and buffer size of a jump-diffusion processing system," Annals of Operations Research, Springer, vol. 217(1), pages 319-335, June.
    2. Bert Zwart, 2015. "Loss rates in the single-server queue with complete rejection," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 299-315, June.

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