IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i3p966-979.html
   My bibliography  Save this article

Existence of an infinite particle limit of stochastic ranking process

Author

Listed:
  • Hattori, Kumiko
  • Hattori, Tetsuya

Abstract

We study a stochastic particle system which models the time evolution of the ranking of books by online bookstores (e.g., Amazon.co.jp). In this system, particles are lined in a queue. Each particle jumps at random jump times to the top of the queue, and otherwise stays in the queue, being pushed toward the tail every time another particle jumps to the top. In an infinite particle limit, the random motion of each particle between its jumps converges to a deterministic trajectory. (This trajectory is actually observed in the ranking data on web sites.) We prove that the (random) empirical distribution of this particle system converges to a deterministic space-time-dependent distribution. A core of the proof is the law of large numbers for dependent random variables.

Suggested Citation

  • Hattori, Kumiko & Hattori, Tetsuya, 2009. "Existence of an infinite particle limit of stochastic ranking process," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 966-979, March.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:3:p:966-979
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(08)00088-4
    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.

    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:spapps:v:119:y:2009:i:3:p:966-979. 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.

    We have no bibliographic references for this item. You can help adding them by using 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/505572/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.