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Asymptotic expansions of defective renewal equations with applications to perturbed risk models and processor sharing queues

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  • Jose Blanchet
  • Bert Zwart

Abstract

We consider asymptotic expansions for defective and excessive renewal equations that are close to being proper. These expansions are applied to the analysis of processor sharing queues and perturbed risk models, and yield approximations that can be useful in applications where moments are computable, but the distribution is not. Copyright Springer-Verlag 2010

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  • Jose Blanchet & Bert Zwart, 2010. "Asymptotic expansions of defective renewal equations with applications to perturbed risk models and processor sharing queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 311-326, October.
    • Handle: RePEc:spr:mathme:v:72:y:2010:i:2:p:311-326
    DOI: 10.1007/s00186-010-0321-6
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    References listed on IDEAS

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    1. Dufresne, Francois & Gerber, Hans U., 1991. "Risk theory for the compound Poisson process that is perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 51-59, March.
    2. Gyllenberg, Mats & Silvestrov, Dmitrii S., 2000. "Nonlinearly perturbed regenerative processes and pseudo-stationary phenomena for stochastic systems," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 1-27, March.
    3. Qiang Zhen & Charles Knessl, 2010. "Asymptotic expansions for the sojourn time distribution in the M/G/1-PS queue," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 201-244, April.
    4. Gyllenberg, Mats & S. Silvestrov, Dmitrii, 2000. "Cramer-Lundberg approximation for nonlinearly perturbed risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 75-90, February.
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    Cited by:

    1. Vatamidou, E. & Adan, I.J.B.F. & Vlasiou, M. & Zwart, B., 2013. "Corrected phase-type approximations of heavy-tailed risk models using perturbation analysis," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 366-378.
    2. Mikael Petersson, 2017. "Quasi-Stationary Asymptotics for Perturbed Semi-Markov Processes in Discrete Time," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1047-1074, December.

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