IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v193y2023ics0167715222002103.html
   My bibliography  Save this article

Right-most position of a last progeny modified time inhomogeneous branching random walk

Author

Listed:
  • Bandyopadhyay, Antar
  • Ghosh, Partha Pratim

Abstract

In this work, we consider a modification of the time inhomogeneous branching random walk, where the driving increment distribution changes over time macroscopically. Following Bandyopadhyay and Ghosh (2021), we give certain independent and identically distributed (i.i.d.) displacements to all the particles at the last generation. We call this process last progeny modified time inhomogeneous branching random walk (LPMTI-BRW). Under very minimal assumptions on the underlying point processes of the displacements, we show that the maximum displacement converges to a non-trivial limit after an appropriate centering which is either linear or linear with a logarithmic correction. Interestingly, the limiting distribution depends only on the first set of increments. We also derive Brunet–Derrida-type results of point process convergence of our LPMTI-BRW to a decorated Poisson point process. As in the case of the maximum, the limiting point process also depends only on the first set of increments. Our proofs are based on a method of coupling the maximum displacement with an appropriate linear statistics, which was introduced by Bandyopadhyay and Ghosh (2021).

Suggested Citation

  • Bandyopadhyay, Antar & Ghosh, Partha Pratim, 2023. "Right-most position of a last progeny modified time inhomogeneous branching random walk," Statistics & Probability Letters, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:stapro:v:193:y:2023:i:c:s0167715222002103
    DOI: 10.1016/j.spl.2022.109697
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715222002103
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2022.109697?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. Thomas Madaule, 2017. "Convergence in Law for the Branching Random Walk Seen from Its Tip," Journal of Theoretical Probability, Springer, vol. 30(1), pages 27-63, March.
    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.

      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:eee:stapro:v:193:y:2023:i:c:s0167715222002103. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

      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.