IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v26y2024i3d10.1007_s11009-024-10097-8.html
   My bibliography  Save this article

Branching Random Walks on $$\mathbb {Z}$$ Z with One Particle Generation Center and Symmetrically Located Absorbing Sources

Author

Listed:
  • Elena Filichkina

    (Lomonosov Moscow State University)

  • Elena Yarovaya

    (Lomonosov Moscow State University)

Abstract

We consider a continuous-time branching random walk (BRW) on a one-dimensional lattice on which there is one center (the lattice point) of particle generation, called branching source. The generation of particles in the branching source is described by a Markov branching process. Some number (finite or infinite, depending on the problem formulation) of absorbing sources is located symmetrically around the branching source. For such configurations of sources we obtain necessary and sufficient conditions for the existence of an isolated positive eigenvalue of the evolution operator. It is shown that, under some additional assumptions, the existence of such an eigenvalue leads to an exponential growth of the number of particles in each point of the lattice.

Suggested Citation

  • Elena Filichkina & Elena Yarovaya, 2024. "Branching Random Walks on $$\mathbb {Z}$$ Z with One Particle Generation Center and Symmetrically Located Absorbing Sources," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-16, September.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:3:d:10.1007_s11009-024-10097-8
    DOI: 10.1007/s11009-024-10097-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-024-10097-8
    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/s11009-024-10097-8?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. Elena B. Yarovaya, 2013. "Branching Random Walks With Several Sources-super-," Mathematical Population Studies, Taylor & Francis Journals, vol. 20(1), pages 14-26, March.
    2. Elena Filichkina & Elena Yarovaya, 2023. "Branching Random Walks with One Particle Generation Center and Possible Absorption at Every Point," Mathematics, MDPI, vol. 11(7), pages 1-16, March.
    3. Elena Chernousova & Yaqin Feng & Ostap Hryniv & Stanislav Molchanov & Joseph Whitmeyer, 2021. "Steady states of lattice population models with immigration," Mathematical Population Studies, Taylor & Francis Journals, vol. 28(2), pages 63-80, April.
    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. Elena Filichkina & Elena Yarovaya, 2023. "Branching Random Walks with One Particle Generation Center and Possible Absorption at Every Point," Mathematics, MDPI, vol. 11(7), pages 1-16, March.
    2. Stanislav Molchanov & Joseph Whitmeyer, 2017. "Stationary distributions in Kolmogorov-Petrovski- Piskunov-type models with an infinite number of particles," Mathematical Population Studies, Taylor & Francis Journals, vol. 24(3), pages 147-160, July.

    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:26:y:2024:i:3:d:10.1007_s11009-024-10097-8. 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.