IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v27y2025i2d10.1007_s11009-025-10179-1.html
   My bibliography  Save this article

Tempered Space-Time Fractional Negative Binomial Process

Author

Listed:
  • Shilpa Garg

    (Central University of Punjab)

  • Ashok Kumar Pathak

    (Central University of Punjab)

  • Aditya Maheshwari

    (Indian Institute of Management Indore)

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.

Suggested Citation

  • Shilpa Garg & Ashok Kumar Pathak & Aditya Maheshwari, 2025. "Tempered Space-Time Fractional Negative Binomial Process," Methodology and Computing in Applied Probability, Springer, vol. 27(2), pages 1-16, June.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:2:d:10.1007_s11009-025-10179-1
    DOI: 10.1007/s11009-025-10179-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-025-10179-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-025-10179-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Rafael Mendoza-Arriaga & Vadim Linetsky, 2016. "Multivariate Subordination Of Markov Processes With Financial Applications," Mathematical Finance, Wiley Blackwell, vol. 26(4), pages 699-747, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rolando Rubilar-Torrealba & Lisandro Fermin & Soledad Torres, 2025. "Modeling Maximum drawdown Records with Piecewise Deterministic Markov Processe in Capital Markets," Papers 2503.23221, arXiv.org.
    2. Patrizia Semeraro, 2022. "Multivariate tempered stable additive subordination for financial models," Mathematics and Financial Economics, Springer, volume 16, number 3, October.
    3. Patrizia Semeraro, 2021. "Multivariate tempered stable additive subordination for financial models," Papers 2105.00844, arXiv.org, revised Sep 2021.
    4. Agostino Capponi & Christoph Frei, 2017. "Systemic Influences on Optimal Equity-Credit Investment," Management Science, INFORMS, vol. 63(8), pages 2756-2771, August.
    5. Qu, Yan & Dassios, Angelos & Zhao, Hongbiao, 2021. "Random variate generation for exponential and gamma tilted stable distributions," LSE Research Online Documents on Economics 108593, London School of Economics and Political Science, LSE Library.
    6. Yakubovich, Yuri, 2021. "A simple proof of the Lévy–Khintchine formula for subordinators," Statistics & Probability Letters, Elsevier, vol. 176(C).
    7. Lijun Bo & Huafu Liao & Yongjin Wang, 2018. "Optimal Credit Investment and Risk Control for an Insurer with Regime-Switching," Papers 1807.05513, arXiv.org.
    8. John R. Birge & Lijun Bo & Agostino Capponi, 2018. "Risk-Sensitive Asset Management and Cascading Defaults," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 1-28, February.
    9. Maheshwari, Aditya, 2023. "Tempered space fractional negative binomial process," Statistics & Probability Letters, Elsevier, vol. 196(C).
    10. Vishwakant Malladi & Rafael Mendoza-Arriaga & Stathis Tompaidis, 2020. "Modeling Dependent Outages of Electric Power Plants," Operations Research, INFORMS, vol. 68(1), pages 1-15, January.
    11. Lijun Bo & Agostino Capponi, 2018. "Portfolio Choice with Market-Credit Risk Dependencies," Papers 1806.07175, arXiv.org.
    12. Tahir Choulli & Catherine Daveloose & Michèle Vanmaele, 2020. "A martingale representation theorem and valuation of defaultable securities," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1527-1564, October.
    13. Tianyao Chen & Xue Cheng & Jingping Yang, 2019. "Common Decomposition of Correlated Brownian Motions and its Financial Applications," Papers 1907.03295, arXiv.org, revised Nov 2020.
    14. Lin, Feng & Peng, Liang & Xie, Jiehua & Yang, Jingping, 2018. "Stochastic distortion and its transformed copula," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 148-166.
    15. Amici, Giovanni & Ballotta, Laura & Semeraro, Patrizia, 2025. "Multivariate additive subordination with applications in finance," European Journal of Operational Research, Elsevier, vol. 321(3), pages 1004-1020.
    16. K. K. Kataria & M. Khandakar, 2021. "On the Long-Range Dependence of Mixed Fractional Poisson Process," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1607-1622, September.
    17. Jie Chen & Liaoyuan Fan & Lingfei Li & Gongqiu Zhang, 2022. "A multidimensional Hilbert transform approach for barrier option pricing and survival probability calculation," Review of Derivatives Research, Springer, vol. 25(2), pages 189-232, July.
    18. Damien Ackerer & Damir Filipović, 2020. "Linear credit risk models," Finance and Stochastics, Springer, vol. 24(1), pages 169-214, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:27:y:2025:i:2:d:10.1007_s11009-025-10179-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.