IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v79y2009i2p145-154.html
   My bibliography  Save this article

Branching on a Sierpinski graph

Author

Listed:
  • Leorato, S.
  • Orsingher, E.

Abstract

The descending motion of particles in a Sierpinski gasket subject to a branching process is examined. The splitting on escape nodes of falling particles makes the event of reaching the base of the gasket possible with positive probability. The r.v.'s Y(k), representing the number of particles reaching level k (that is the k-th generation) is the main object of our analysis. The transition probabilities, the means and variances of Y(k) are obtained explicitly with a number of recursive formulas concerning the probability generating functions , k>=1. A section is also devoted to the analysis of extinction probabilities for the branching process developing in this specific fractal set.

Suggested Citation

  • Leorato, S. & Orsingher, E., 2009. "Branching on a Sierpinski graph," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 145-154, January.
  • Handle: RePEc:eee:stapro:v:79:y:2009:i:2:p:145-154
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(08)00358-1
    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. Jones, Owen Dafydd, 1996. "Transition probabilities for the simple random walk on the Sierpinski graph," Stochastic Processes and their Applications, Elsevier, vol. 61(1), pages 45-69, January.
    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. Takashi Kumagai & Chikara Nakamura, 2018. "Lamplighter Random Walks on Fractals," Journal of Theoretical Probability, Springer, vol. 31(1), pages 68-92, March.
    2. Grabner, Peter J. & Woess, Wolfgang, 1997. "Functional iterations and periodic oscillations for simple random walk on the Sierpinski graph," Stochastic Processes and their Applications, Elsevier, vol. 69(1), pages 127-138, July.

    More about this item

    Statistics

    Access and download statistics

    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:79:y:2009:i:2:p:145-154. 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.