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Generalized Fractional Negative Binomial Process

Probability 2023-04-21 v1

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.

Keywords

Cite

@article{arxiv.2304.10487,
  title  = {Generalized Fractional Negative Binomial Process},
  author = {Ritik Soni and Ashok Kumar Pathak},
  journal= {arXiv preprint arXiv:2304.10487},
  year   = {2023}
}
R2 v1 2026-06-28T10:12:48.310Z