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The fractional non-homogeneous Poisson process

Nikolai Leonenko, Enrico Scalas () and Mailan Trinh

Statistics & Probability Letters, 2017, vol. 120, issue C, 147-156

Abstract: We introduce a non-homogeneous fractional Poisson process by replacing the time variable in the fractional Poisson process of renewal type with an appropriate function of time. We characterize the resulting process by deriving its non-local governing equation. We further compute the first and second moments of the process. Eventually, we derive the distribution of arrival times. Constant reference is made to previous known results in the homogeneous case and to how they can be derived from the specialization of the non-homogeneous process.

Keywords: Fractional point processes; Lévy processes; Time-change; Subordination (search for similar items in EconPapers)
Date: 2017
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Handle: RePEc:eee:stapro:v:120:y:2017:i:c:p:147-156