IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v331y2004i3p391-408.html
   My bibliography  Save this article

Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker–Planck equations

Author

Listed:
  • Frank, T.D.

Abstract

We discuss two fundamental aspects of Fokker–Planck equations that are nonlinear with respect to probability densities. First, we show that evolution equations of this kind describe processes involving stochastic feedback and interpret stochastic feedback processes in terms of hitchhiker processes and path integral solutions. Second, we demonstrate that nonlinear Fokker–Planck equations can be interpreted as linear Fokker–Planck equations describing nonlinear families of Markov diffusion processes. We exploit this finding in order to derive complete hierarchies of probability densities from nonlinear Fokker–Planck equations.

Suggested Citation

  • Frank, T.D., 2004. "Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker–Planck equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(3), pages 391-408.
    • Handle: RePEc:eee:phsmap:v:331:y:2004:i:3:p:391-408
    DOI: 10.1016/j.physa.2003.09.056
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437103009051
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2003.09.056?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Hashemi, M.S., 2015. "Group analysis and exact solutions of the time fractional Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 141-149.
    2. McCauley, Joseph L., 2007. "A comment on the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker–Planck equations” by T.D. Frank," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 445-452.

    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:phsmap:v:331:y:2004:i:3:p:391-408. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.