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