IDEAS home Printed from https://ideas.repec.org/a/taf/lstaxx/v52y2023i4p988-1011.html
   My bibliography  Save this article

Exact convergence rate of the local limit theorem for a branching random walk in a time-dependent random environment on d-dimensional integer lattice

Author

Listed:
  • Zhiqiang Gao
  • Xiaoyan Zhang

Abstract

Consider a branching random walk in Zd, where both the offspring distribution and the displacement law vary with generation time. For each x∈Zd, let Zn(x) denote the number of particles of n-th generation located at x. We derive exact convergence rate of the local limit theorem for the counting measure Zn(x). This generalizes the result obtained in Gao (2017, SPA) by adding the random environment affects, and improves it by weakening the moment condition required for the offspring distribution.

Suggested Citation

  • Zhiqiang Gao & Xiaoyan Zhang, 2023. "Exact convergence rate of the local limit theorem for a branching random walk in a time-dependent random environment on d-dimensional integer lattice," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(4), pages 988-1011, February.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:4:p:988-1011
    DOI: 10.1080/03610926.2021.1921807
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/03610926.2021.1921807
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/03610926.2021.1921807?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.

    More about this item

    Statistics

    Access and download statistics

    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:taf:lstaxx:v:52:y:2023:i:4:p:988-1011. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/lsta .

    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.