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On the asymptotic behaviour of the covariance function of the rewards of a multivariate renewal–reward process

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  • Aliyev, Rovshan
  • Bayramov, Veli

Abstract

In this study, a renewal–reward process with multivariate rewards is investigated and an asymptotic expansion for the covariance function of the rewards is derived. The remainder term of the result in Patch et al. (2015) is sharpened from the o(1) to o(t−k). Moreover, asymptotic expansions as t→∞ with the remainder term o(t−k) for the mathematical expectation and variance of the renewal–reward process also are obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:127:y:2017:i:c:p:138-149
    DOI: 10.1016/j.spl.2017.04.011
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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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.

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