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A correction term for the covariance of renewal-reward processes with multivariate rewards

Author

Listed:
  • Patch, Brendan
  • Nazarathy, Yoni
  • Taimre, Thomas

Abstract

We consider a renewal-reward process with multivariate rewards. Such a process is constructed from an i.i.d. sequence of time periods, to each of which there is associated a multivariate reward vector. The rewards in each time period may depend on each other and on the period length, but not on the other time periods. Rewards are accumulated to form a vector valued process that exhibits jumps in all coordinates simultaneously, only at renewal epochs.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:102:y:2015:i:c:p:1-7
    DOI: 10.1016/j.spl.2015.03.005
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    References listed on IDEAS

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    1. Badila, E.S. & Boxma, O.J. & Resing, J.A.C., 2015. "Two parallel insurance lines with simultaneous arrivals and risks correlated with inter-arrival times," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 48-61.
    2. 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.
    2. 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.

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