IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v165y2020ics0167715220301632.html
   My bibliography  Save this article

Convergence rate to equilibrium in Wasserstein distance for reflected jump–diffusions

Author

Listed:
  • Sarantsev, Andrey

Abstract

Convergence rate to the stationary distribution for continuous-time Markov processes can be studied using Lyapunov functions. Recent work by the author provided explicit rates of convergence in special case of a reflected jump–diffusion on a half-line. These results are proved for total variation distance and its generalizations: measure distances defined by test functions regardless of their continuity. Here we prove similar results for Wasserstein distance, convergence in which is related to convergence for continuous test functions. In some cases, including the reflected Ornstein–Uhlenbeck process, we get faster exponential convergence rates for Wasserstein distance than for total variation distance.

Suggested Citation

  • Sarantsev, Andrey, 2020. "Convergence rate to equilibrium in Wasserstein distance for reflected jump–diffusions," Statistics & Probability Letters, Elsevier, vol. 165(C).
    • Handle: RePEc:eee:stapro:v:165:y:2020:i:c:s0167715220301632
    DOI: 10.1016/j.spl.2020.108860
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715220301632
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2020.108860?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. Guodong Pang & Andrey Sarantsev & Yana Belopolskaya & Yuri Suhov, 2020. "Stationary distributions and convergence for M/M/1 queues in interactive random environment," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 357-392, April.
    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. Sarantsev, Andrey, 2021. "Sub-exponential rate of convergence to equilibrium for processes on the half-line," Statistics & Probability Letters, Elsevier, vol. 175(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.

      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:165:y:2020:i:c:s0167715220301632. 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.