IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v122y2012i4p1988-1997.html
   My bibliography  Save this article

On Lundh’s percolation diffusion

Author

Listed:
  • Carroll, Tom
  • O’Donovan, Julie
  • Ortega-Cerdà, Joaquim

Abstract

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable configurations are generated with positive probability, Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.

Suggested Citation

  • Carroll, Tom & O’Donovan, Julie & Ortega-Cerdà, Joaquim, 2012. "On Lundh’s percolation diffusion," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1988-1997.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:4:p:1988-1997
    DOI: 10.1016/j.spa.2011.12.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414911003188
    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. Lundh, Torbjörn, 2001. "Percolation diffusion," Stochastic Processes and their Applications, Elsevier, vol. 95(2), pages 235-244, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Mimica, Ante & Vondraček, Zoran, 2014. "Unavoidable collections of balls for isotropic Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1303-1334.

    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:122:y:2012:i:4:p:1988-1997. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.