English

Tempered space-time fractional negative binomial process

Probability 2024-09-12 v1

Abstract

In this paper, we define a tempered space-time fractional negative binomial process (TSTFNBP) by subordinating the fractional Poisson process with an independent tempered Mittag-Leffler L\'{e}vy subordinator. We study its distributional properties and its connection to partial differential equations. We derive the asymptotic behavior of its fractional order moments and long-range dependence property. It is shown that the TSTFNBP exhibits overdispersion. We also obtain some results related to the first-passage time.

Keywords

Cite

@article{arxiv.2409.07044,
  title  = {Tempered space-time fractional negative binomial process},
  author = {Shilpa and Ashok Kumar Pathak and Aditya Maheshwari},
  journal= {arXiv preprint arXiv:2409.07044},
  year   = {2024}
}

Comments

11 pages

R2 v1 2026-06-28T18:40:47.116Z