IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v36y2023i4d10.1007_s10959-023-01268-3.html
   My bibliography  Save this article

Fractional Poisson Processes of Order k and Beyond

Author

Listed:
  • Neha Gupta

    (Indian Statistical Institute Delhi)

  • Arun Kumar

    (Indian Institute of Technology Ropar)

Abstract

In this article, we introduce fractional Poisson fields of order k in n-dimensional Euclidean space of positive real valued vectors. We also work on time-fractional Poisson process of order k, space-fractional Poisson processes of order k and a tempered version of time-space fractional Poisson processes of order k. We discuss generalized fractional Poisson processes of order k in terms of Bernstein functions. These processes are defined in terms of fractional compound Poisson processes. The time-fractional Poisson process of order k naturally generalizes the Poisson process and the Poisson process of order k to a heavy-tailed waiting-times counting process. The space-fractional Poisson process of order k allows on average an infinite number of arrivals in any interval. We derive the marginal probabilities governing difference–differential equations of the introduced processes. We also provide the Watanabe martingale characterization for some time-changed Poisson processes.

Suggested Citation

  • Neha Gupta & Arun Kumar, 2023. "Fractional Poisson Processes of Order k and Beyond," Journal of Theoretical Probability, Springer, vol. 36(4), pages 2165-2191, December.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:4:d:10.1007_s10959-023-01268-3
    DOI: 10.1007/s10959-023-01268-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-023-01268-3
    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/s10959-023-01268-3?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.

    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:jotpro:v:36:y:2023:i:4:d:10.1007_s10959-023-01268-3. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.