IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v120y2010i5p590-604.html
   My bibliography  Save this article

From one dimensional diffusions to symmetric Markov processes

Author

Listed:
  • Fukushima, Masatoshi

Abstract

For an absorbing diffusion X0 on a one dimensional regular interval I with no killing inside, the Dirichlet form of X0 on L2(I;m) and its extended Dirichlet space are identified in terms of the canonical scale s of X0, where m is the canonical measure of X0. All possible symmetric extensions of X0 will then be considered in relation to the active reflected Dirichlet space of X0. Furthermore quite analogous considerations will be made for possible symmetric extensions of a specific diffusion in a higher dimension, namely, a time changed transient reflecting Brownian motion on a closed domain of , possessing two branches of infinite cones.

Suggested Citation

  • Fukushima, Masatoshi, 2010. "From one dimensional diffusions to symmetric Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 590-604, May.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:5:p:590-604
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(10)00019-0
    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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chen, Zhen-Qing & Fukushima, Masatoshi, 2015. "One-point reflection," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1368-1393.

    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:120:y:2010:i:5:p:590-604. 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.