Generalized Fractional Negative Binomial Process

Ritik Soni; Ashok Kumar Pathak

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arXiv · 2304.10487

Generalized Fractional Negative Binomial Process

Ritik Soni·Ashok Kumar Pathak

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Abstract

In this paper, we introduce a generalized fractional negative binomial process (GFNBP) by time changing the fractional Poisson process with an independent Mittag-Leffler (ML) Levy subordinator. We study its distributional properties and its connection to PDEs. We examine the long-range dependence (LRD) property of the GFNBP and show that it is not infinitely divisible. The space fractional and the non-homogeneous variants of the GFNBP are explored. Finally, simulated sample paths for the ML Levy subordinator and the GFNBP are also presented.

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Ritik Soni, Ashok Kumar Pathak. 2023-04-20. Generalized Fractional Negative Binomial Process. https://arxiv.org/abs/2304.10487

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