IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v177y2024ics0304414924001637.html
   My bibliography  Save this article

Quasi-stationary distribution for continuous-state branching processes with competition

Author

Listed:
  • Li, Pei-Sen
  • Wang, Jian
  • Zhou, Xiaowen

Abstract

We study quasi-stationary distribution of the continuous-state branching process with competition introduced by Berestycki et al. (2018). This process is defined as the unique strong solution to a stochastic integral equation with jumps. An important example is the logistic branching process proposed by Lambert (2005). We establish the strong Feller property, trajectory Feller property, Lyapunov condition, weak Feller property and irreducibility, respectively. These properties together allow us to prove that if the competition is strong enough near +∞, then there is a unique quasi-stationary distribution, which attracts all initial distributions with exponential rates.

Suggested Citation

  • Li, Pei-Sen & Wang, Jian & Zhou, Xiaowen, 2024. "Quasi-stationary distribution for continuous-state branching processes with competition," Stochastic Processes and their Applications, Elsevier, vol. 177(C).
  • Handle: RePEc:eee:spapps:v:177:y:2024:i:c:s0304414924001637
    DOI: 10.1016/j.spa.2024.104457
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414924001637
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spa.2024.104457?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. Champagnat, Nicolas & Villemonais, Denis, 2021. "Lyapunov criteria for uniform convergence of conditional distributions of absorbed Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 51-74.
    2. Luo, Dejun & Wang, Jian, 2019. "Refined basic couplings and Wasserstein-type distances for SDEs with Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3129-3173.
    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. Bao, Jianhai & Wang, Jian, 2022. "Coupling approach for exponential ergodicity of stochastic Hamiltonian systems with Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 114-142.
    2. Michel Benaïm & Nicolas Champagnat & William Oçafrain & Denis Villemonais, 2023. "Transcritical Bifurcation for the Conditional Distribution of a Diffusion Process," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1555-1571, September.
    3. Wang, Tao, 2022. "Ergodic convergence rates for time-changed symmetric Lévy processes in dimension one," Statistics & Probability Letters, Elsevier, vol. 183(C).
    4. Popov, Serguei & Shcherbakov, Vadim & Volkov, Stanislav, 2022. "Linear competition processes and generalized Pólya urns with removals," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 125-152.
    5. Liang, Mingjie & Wang, Jian, 2020. "Gradient estimates and ergodicity for SDEs driven by multiplicative Lévy noises via coupling," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 3053-3094.
    6. Shukai Chen & Rongjuan Fang & Xiangqi Zheng, 2023. "Wasserstein-Type Distances of Two-Type Continuous-State Branching Processes in Lévy Random Environments," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1572-1590, September.
    7. Velleret, Aurélien, 2022. "Unique quasi-stationary distribution, with a possibly stabilizing extinction," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 98-138.
    8. Huang, Lu-Jing & Majka, Mateusz B. & Wang, Jian, 2022. "Strict Kantorovich contractions for Markov chains and Euler schemes with general noise," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 307-341.
    9. Franziska Kühn, 2021. "Schauder Estimates for Poisson Equations Associated with Non-local Feller Generators," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1506-1578, September.
    10. Jianhai Bao & Jian Wang, 2023. "Coupling methods and exponential ergodicity for two‐factor affine processes," Mathematische Nachrichten, Wiley Blackwell, vol. 296(5), pages 1716-1736, May.

    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:spapps:v:177:y:2024:i:c:s0304414924001637. 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/505572/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.