IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i8p2625-2644.html
   My bibliography  Save this article

Decomposition and convergence for tree martingales

Author

Listed:
  • He, Tong-jun
  • Shen, Yi

Abstract

In this paper, the authors firstly construct a graph-theoretic decomposition of an index set for tree martingales, and based on this decomposition, they give a locally finite tree martingale's notion and a tree martingale decomposition theorem. Secondly, they establish some relations between the locally finite tree martingales and the multiparameter martingales, and furthermore the convergence of tree martingales is shown by using the multiparameter martingale theory of Cairoli-Walsh. Finally, with some mild conditions, two inequalities for tree martingales are obtained by using their decomposition theorem and multiparameter martingale theory.

Suggested Citation

  • He, Tong-jun & Shen, Yi, 2009. "Decomposition and convergence for tree martingales," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2625-2644, August.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:8:p:2625-2644
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(09)00027-1
    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. Häggström, Olle, 1995. "Random-cluster measures and uniform spanning trees," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 267-275, October.
    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. Häggström, Olle, 2001. "Coloring percolation clusters at random," Stochastic Processes and their Applications, Elsevier, vol. 96(2), pages 213-242, December.

    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:8:p:2625-2644. 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/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.