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A second-order approximation for the variance of a renewal reward process

Author

Listed:
  • Brown, Mark
  • Solomon, Herbert

Abstract

Let {C(t), t [greater-or-equal, slanted] 0} be a renewal reward process. We obtain the approximation Var C(t) = ct + d + o(1), and explicitly identify c and d.

Suggested Citation

  • Brown, Mark & Solomon, Herbert, 1975. "A second-order approximation for the variance of a renewal reward process," Stochastic Processes and their Applications, Elsevier, vol. 3(3), pages 301-314, July.
    • Handle: RePEc:eee:spapps:v:3:y:1975:i:3:p:301-314
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    Citations

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    Cited by:

    1. Landy Rabehasaina & Jae-Kyung Woo, 2018. "On a multivariate renewal-reward process involving time delays and discounting: applications to IBNR processes and infinite server queues," Queueing Systems: Theory and Applications, Springer, vol. 90(3), pages 307-350, December.
    2. Hautphenne, Sophie & Kerner, Yoav & Nazarathy, Yoni & Taylor, Peter, 2015. "The intercept term of the asymptotic variance curve for some queueing output processes," European Journal of Operational Research, Elsevier, vol. 242(2), pages 455-464.
    3. Khaniyev, T. & Kesemen, T. & Aliyev, R. & Kokangul, A., 2008. "Asymptotic expansions for the moments of a semi-Markovian random walk with exponential distributed interference of chance," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 785-793, April.
    4. Aynura Poladova & Salih Tekin & Tahir Khaniyev, 2020. "A novel replacement policy for a linear deteriorating system using stochastic process with dependent components," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(3), pages 381-396, May.
    5. Xin Liu & Qi Gong & Vidyadhar G. Kulkarni, 2015. "A Stochastic Model of Order Book Dynamics using Bouncing Geometric Brownian Motions," Papers 1511.04096, arXiv.org, revised Mar 2016.
    6. Aliyev, Rovshan & Bayramov, Veli, 2017. "On the asymptotic behaviour of the covariance function of the rewards of a multivariate renewal–reward process," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 138-149.
    7. Patch, Brendan & Nazarathy, Yoni & Taimre, Thomas, 2015. "A correction term for the covariance of renewal-reward processes with multivariate rewards," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 1-7.

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