IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v169y2021ics0167715220302674.html
   My bibliography  Save this article

Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures

Author

Listed:
  • Hille, Sander C.
  • Szarek, Tomasz
  • Worm, Daniel T.H.
  • Ziemlańska, Maria A.

Abstract

Various equicontinuity properties for families of Markov operators have been – and still are – used in the study of existence and uniqueness of invariant probability for these operators, and of asymptotic stability. We prove a general result on equivalence of equicontinuity concepts. It allows comparing results in the literature and switching from one view on equicontinuity to another, which is technically convenient in proofs. More precisely, the characterisation is based on a ‘Schur-like property’ for measures: if a sequence of finite signed Borel measures on a Polish space is such that it is bounded in total variation norm and such that for each bounded Lipschitz function the sequence of integrals of this function with respect to these measures converges, then the sequence converges in dual bounded Lipschitz norm to a measure.

Suggested Citation

  • Hille, Sander C. & Szarek, Tomasz & Worm, Daniel T.H. & Ziemlańska, Maria A., 2021. "Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures," Statistics & Probability Letters, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:stapro:v:169:y:2021:i:c:s0167715220302674
    DOI: 10.1016/j.spl.2020.108964
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715220302674
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2020.108964?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. Czapla, Dawid, 2018. "A criterion on asymptotic stability for partially equicontinuous Markov operators," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3656-3678.
    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.

      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:169:y:2021:i:c:s0167715220302674. 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.