IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v57y2002i1p17-22.html
   My bibliography  Save this article

Donkey walk and Dirichlet distributions

Author

Listed:
  • Letac, Gérard

Abstract

The donkey performs a random walk (Xn)n[greater-or-equal, slanted]0 inside a tetrahedron with vertices A1,...,Ad as follows. For r=1,...,d and t=0,1,..., at time dt+r the donkey moves from the point Xdt+r-1 to a point Xdt+r such that the barycentric coordinates of Xdt+r with respect to A1,...,Ar-1,Xdt+r-1,Ar+1,...,Ad have a Dirichlet distribution depending on r. When the parameters are properly chosen, we compute the stationary distributions of the d homogeneous Markov chains (Xdt+r)t[greater-or-equal, slanted]0. For instance, if Xdt+r is uniformly chosen in the tetrahedron with vertices A1,...,Ar-1,Xdt+r-1,Ar+1,...,Ad then the stationary distribution of (Xdt)t[greater-or-equal, slanted]0 is Dirichlet with parameters (d,d-1,...,1).

Suggested Citation

  • Letac, Gérard, 2002. "Donkey walk and Dirichlet distributions," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 17-22, March.
    • Handle: RePEc:eee:stapro:v:57:y:2002:i:1:p:17-22
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(02)00027-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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.
    2. Marco Scarsini & Gérard Letac, 1998. "Random nested tetrahedra," Post-Print hal-00541756, HAL.
    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. McKinlay, Shaun, 2017. "On beta distributed limits of iterated linear random functions," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 33-41.
    2. Gupta, Rameshwar D. & Richards, Donald St. P., 2002. "Moment Properties of the Multivariate Dirichlet Distributions," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 240-262, July.
    3. Letac, Gérard & Massam, Hélène & Richards, Donald, 2001. "An Expectation Formula for the Multivariate Dirichlet Distribution," Journal of Multivariate Analysis, Elsevier, vol. 77(1), pages 117-137, April.
    4. 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.
    5. 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).
    6. 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.

    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:57:y:2002:i:1:p:17-22. 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.