IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v145y2019icp1-11.html
   My bibliography  Save this article

On the asymptotic behavior of the Diaconis–Freedman chain on [0,1]

Author

Listed:
  • Ladjimi, Fetima
  • Peigné, Marc

Abstract

We describe the asymptotic behavior of the Diaconis–Freedman chain on [0,1], using technics developed to study iterated Lipschitz functions systems with possibly place dependent probabilities. Under some general conditions on this family of probabilities and using quasi-compact linear operators technics, we obtain a necessary and sufficient condition for the uniqueness of the stationary probability measure for this chain and explore the case when it does not hold.

Suggested Citation

  • Ladjimi, Fetima & Peigné, Marc, 2019. "On the asymptotic behavior of the Diaconis–Freedman chain on [0,1]," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 1-11.
  • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:1-11
    DOI: 10.1016/j.spl.2018.05.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715218302062
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2018.05.019?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. Stoyanov, Jordan & Pirinsky, Christo, 2000. "Random motions, classes of ergodic Markov chains and beta distributions," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 293-304, November.
    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. Pacheco-González, Carlos G., 2009. "Ergodicity of a bounded Markov chain with attractiveness towards the centre," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2177-2181, October.
    2. Liu, Yujie & Niu, Minwen & Yao, Dacheng & Zhang, Hanqin, 2022. "Stationary distributions and ergodicity of reflection-type Markov chains," Statistics & Probability Letters, Elsevier, vol. 189(C).
    3. McKinlay, Shaun, 2017. "On beta distributed limits of iterated linear random functions," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 33-41.
    4. Letac, Gérard, 2002. "Donkey walk and Dirichlet distributions," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 17-22, March.

    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:145:y:2019:i:c:p:1-11. 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.