IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v118y2008i7p1159-1189.html
   My bibliography  Save this article

Localization of favorite points for diffusion in a random environment

Author

Listed:
  • Cheliotis, Dimitris

Abstract

For a diffusion Xt in a one-dimensional Wiener medium W, it is known that there is a certain process (br(W))r>=0 that depends only on the environment, so that Xt-blogt(W) converges in distribution as t-->[infinity]. The paths of b are step functions. Denote by FX(t) the point with the most local time for the diffusion at time t. We prove that, modulo a relatively small time change, the paths of the processes (br(W))r>=0, (FX(er))r>=0 are close after some large r.

Suggested Citation

  • Cheliotis, Dimitris, 2008. "Localization of favorite points for diffusion in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 118(7), pages 1159-1189, July.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:7:p:1159-1189
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(07)00137-8
    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. Hu, Yueyun, 2000. "Tightness of localization and return time in random environment," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 81-101, March.
    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. Pierre Andreoletti & Roland Diel, 2011. "Limit Law of the Local Time for Brox’s Diffusion," Journal of Theoretical Probability, Springer, vol. 24(3), pages 634-656, September.
    2. Diel, Roland, 2011. "Almost sure asymptotics for the local time of a diffusion in Brownian environment," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2303-2330, October.
    3. Gutierrez-Pavón, Jonathan & Pacheco, Carlos G., 2020. "A density for the local time of the Brox diffusion," Statistics & Probability Letters, Elsevier, vol. 163(C).
    4. Carlos G. Pacheco & Mariana Pérez-Rojas, 2022. "Excursions of the Brox Diffusion," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1479-1500, September.

    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. Andreoletti, Pierre, 2006. "On the concentration of Sinai's walk," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1377-1408, October.
    2. Diel, Roland, 2011. "Almost sure asymptotics for the local time of a diffusion in Brownian environment," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2303-2330, October.
    3. Carlos G. Pacheco & Mariana Pérez-Rojas, 2022. "Excursions of the Brox Diffusion," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1479-1500, September.

    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:118:y:2008:i:7:p:1159-1189. 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.