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Tempered space fractional negative binomial process

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  • Maheshwari, Aditya

Abstract

In this paper, we define a tempered space fractional negative binomial process (TSFNBP) by replacing the Poisson process by a tempered space fractional Poisson process (TSFPP) in the gamma subordinated form of the negative binomial process. We studied its distributional properties, long-range dependence (LRD) property and its connection with pde’s. The LRD property for the TSFPP process is also investigated. Finally, we present simulated sample paths for both the TSFPP and the TSFNBP.

Suggested Citation

  • Maheshwari, Aditya, 2023. "Tempered space fractional negative binomial process," Statistics & Probability Letters, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:stapro:v:196:y:2023:i:c:s0167715223000238
    DOI: 10.1016/j.spl.2023.109799
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    References listed on IDEAS

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    1. L. Beghin & P. Vellaisamy, 2018. "Space-Fractional Versions of the Negative Binomial and Polya-Type Processes," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 463-485, June.
    2. A. Maheshwari & P. Vellaisamy, 2019. "Fractional Poisson Process Time-Changed by Lévy Subordinator and Its Inverse," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1278-1305, September.
    3. Orsingher, Enzo & Polito, Federico, 2012. "The space-fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 852-858.
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