Tempered space-time fractional negative binomial process

Shilpa; Ashok Kumar Pathak; Aditya Maheshwari

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arXiv · 2409.07044

Tempered space-time fractional negative binomial process

Shilpa·Ashok Kumar Pathak·Aditya Maheshwari

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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.

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Shilpa, Ashok Kumar Pathak, Aditya Maheshwari. 2024-09-11. Tempered space-time fractional negative binomial process. https://arxiv.org/abs/2409.07044

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