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

M. Karamzadeh, A.R. Soltani and H.A. Mardani-Fard

Statistics & Probability Letters, 2020, vol. 158, issue C

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.

Keywords: Multivariate renewal processes; Synchronization probabilities; Laplace transform; Renewal function; Long run limiting values (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2019.108658

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