Tempered space-time fractional negative binomial process

Aditya Maheshwari; Ashok Kumar Pathak; Shilpa

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Tempered space-time fractional negative binomial process

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arxiv 2409.07044 v1 pith:U6RO5UDU submitted 2024-09-11 math.PR

Shilpa , Ashok Kumar Pathak , Aditya Maheshwari This is my paper · ORCID

classification math.PR

keywords fractionalprocesstemperedbinomialnegativespace-timetstfnbpasymptotic

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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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