Tempered Space-Time Fractional Negative Binomial Process

Shilpa Garg (), Ashok Kumar Pathak () and Aditya Maheshwari ()
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Shilpa Garg: Central University of Punjab
Ashok Kumar Pathak: Central University of Punjab
Aditya Maheshwari: Indian Institute of Management Indore

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 2, 1-16

Abstract: 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 Lévy subordinator. We study its distributional properties and its connection to partial differential equations. We derive the asymptotic behavior of fractional order moments of tempered Mittag-Leffler Lévy subordinator, using which we obtain the mean, variance, and autocovariance of the TSTFNBP. It is shown that the TSTFNBP exhibits overdispersion and long-range dependence property. At last, we present some simulations for sample paths of the fractional Poisson process subordinated by tempered stable subordinator and for the TSTFNBP.

Keywords: Fractional Poisson process; Tempered Mittag-Leffler subordinator; Fractional moments; Long-range dependence; PDEs; Primary: 60G22; 60G51; 91B05; Secondary: 60G55; 60E05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10179-1

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