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On a class of spatial renewal processes: Renewal processes synchronization probabilities

Author

Listed:
  • Karamzadeh, M.
  • Soltani, A.R.
  • Mardani-Fard, H.A.

Abstract

We mainly focus on the sojourn boxes in spatial renewal processes. On sojourn boxes, the components of a multivariate renewal process are synced together. We provide formulations for the probability that the components to be synced at a multivariate time epoch, and for the average number of synced cases. Then, we introduce a new spatial renewal process by restricting a spatial renewal process to its sojourn boxes, and derive the limiting behavior of the corresponding multivariate renewal function, and cumulative function of synced probability along rays initiated from the origin. Examples are provided as well.

Suggested Citation

  • Karamzadeh, M. & Soltani, A.R. & Mardani-Fard, H.A., 2020. "On a class of spatial renewal processes: Renewal processes synchronization probabilities," Statistics & Probability Letters, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:stapro:v:158:y:2020:i:c:s0167715219303049
    DOI: 10.1016/j.spl.2019.108658
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    References listed on IDEAS

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    1. Royi Jacobovic & Offer Kella, 2019. "Asymptotic independence of regenerative processes with a special dependence structure," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 139-152, October.
    2. Mallor, F. & Omey, E. & Santos, J., 2007. "Multivariate weighted renewal functions," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 30-39, January.
    3. Soltani, A.R. & Ghasemi, H., 2014. "Semi-Markov and reward fields," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 71-76.
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