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<p>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.</p>

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Tempered Space-Time Fractional Negative Binomial Process

  • 期刊论文

  • 发表日期：

    2025年6月13日

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  • Shilpa Garg,
  • Ashok Kumar Pathak,
  • Aditya Maheshwari

摘要

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.