IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v36y2023i3d10.1007_s10959-022-01216-7.html
   My bibliography  Save this article

Transcritical Bifurcation for the Conditional Distribution of a Diffusion Process

Author

Listed:
  • Michel Benaïm

    (Université de Neuchâtel)

  • Nicolas Champagnat

    (Université de Lorraine, CNRS, Inria, IECL)

  • William Oçafrain

    (Université de Lorraine, CNRS, Inria, IECL)

  • Denis Villemonais

    (Université de Lorraine, CNRS, Inria, IECL)

Abstract

In this article, we describe a simple class of models of absorbed diffusion processes with parameter, whose conditional law exhibits a transcritical bifurcation. Our proofs are based on the description of the set of quasi-stationary distributions for general two-clusters reducible processes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:3:d:10.1007_s10959-022-01216-7
    DOI: 10.1007/s10959-022-01216-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-022-01216-7
    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/s10959-022-01216-7?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. van Doorn, Erik A. & Pollett, Philip K., 2013. "Quasi-stationary distributions for discrete-state models," European Journal of Operational Research, Elsevier, vol. 230(1), pages 1-14.
    3. Hening, Alexandru & Kolb, Martin, 2019. "Quasistationary distributions for one-dimensional diffusions with singular boundary points," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1659-1696.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Castro, Matheus M. & Lamb, Jeroen S.W. & Olicón-Méndez, Guillermo & Rasmussen, Martin, 2024. "Existence and uniqueness of quasi-stationary and quasi-ergodic measures for absorbing Markov chains: A Banach lattice approach," Stochastic Processes and their Applications, Elsevier, vol. 173(C).

    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. Velleret, Aurélien, 2022. "Unique quasi-stationary distribution, with a possibly stabilizing extinction," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 98-138.
    2. Economou, A. & Gómez-Corral, A. & López-García, M., 2015. "A stochastic SIS epidemic model with heterogeneous contacts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 78-97.
    3. Mikael Petersson, 2017. "Quasi-Stationary Asymptotics for Perturbed Semi-Markov Processes in Discrete Time," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1047-1074, December.
    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. Artalejo, J.R. & Economou, A. & Lopez-Herrero, M.J., 2015. "The stochastic SEIR model before extinction: Computational approaches," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1026-1043.
    6. Corujo, Josué, 2021. "Dynamics of a Fleming–Viot type particle system on the cycle graph," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 57-91.
    7. Claude Lefèvre & Matthieu Simon, 2022. "On the Risk of Ruin in a SIS Type Epidemic," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 939-961, June.
    8. Leżaj, Łukasz, 2024. "Non-symmetric stable processes: Dirichlet heat kernel, Martin kernel and Yaglom limit," Stochastic Processes and their Applications, Elsevier, vol. 174(C).
    9. 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.
    10. He, Guoman & Zhang, Hanjun & Zhu, Yixia, 2019. "On the quasi-ergodic distribution of absorbing Markov processes," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 116-123.
    11. Ravner, Liron, 2014. "Equilibrium arrival times to a queue with order penalties," European Journal of Operational Research, Elsevier, vol. 239(2), pages 456-468.

    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:3:d:10.1007_s10959-022-01216-7. 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.