IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v160y2023icp218-264.html
   My bibliography  Save this article

Strong Gaussian approximation of metastable density-dependent Markov chains on large time scales

Author

Listed:
  • Prodhomme, Adrien

Abstract

We consider density-dependent Markov chains converging, as the scale parameter K>0 goes to infinity, to the solution of an ODE admitting an exponentially stable equilibrium point. We provide a new strong approximation of the density by a Gaussian process, based on a construction of Kurtz using the Komlós–Major–Tusnády theorem. We show that given any threshold ɛ(K)≪1 greater than a multiple of log(K)/K, the time the error needs to reach ɛ(K) is at least of order exp(VKɛ(K)), for some V>0. We discuss consequences on moderate deviations, applications to a logistic birth-and-death process conditioned to survive and to an epidemic model.

Suggested Citation

  • Prodhomme, Adrien, 2023. "Strong Gaussian approximation of metastable density-dependent Markov chains on large time scales," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 218-264.
  • Handle: RePEc:eee:spapps:v:160:y:2023:i:c:p:218-264
    DOI: 10.1016/j.spa.2023.01.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414923000303
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spa.2023.01.018?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.

    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:160:y:2023:i:c:p:218-264. 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: 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.