IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v20y1985i2p323-331.html
   My bibliography  Save this article

Noise can create periodic behavior and stabilize nonlinear diffusions

Author

Listed:
  • Scheutzow, Michael

Abstract

It is shown that unlike nondegenerate (linear) diffusion processes, nonlinear diffusion processes can have a periodic law. We provide an example of a nonlinear diffusion for which periodic behavior is even created by the noise, i.e. no periodicity occurs when the noise is turned off. In the second part of the paper we give an example of a one-dimensional nonlinear diffusion which can be stabilized by noise. Finally we show also that the N-dimensional (N >= 2) 'linear' diffusion approximations of that system are stabilized by noise.

Suggested Citation

  • Scheutzow, Michael, 1985. "Noise can create periodic behavior and stabilize nonlinear diffusions," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 323-331, September.
    • Handle: RePEc:eee:spapps:v:20:y:1985:i:2:p:323-331
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(85)90219-4
    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. Alexander Harin, 2021. "Auto-Transformations of the Probability Density Functions," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 7(3), pages 167-178, 07-2021.
    2. Harin, Alexander, 2018. "Forbidden zones for the expectation. New mathematical results for behavioral and social sciences," MPRA Paper 86650, University Library of Munich, Germany.
    3. Harin, Alexander, 2019. "Forbidden zones for the expectations of measurement data and problems of behavioral economics," MPRA Paper 91368, University Library of Munich, Germany.
    4. Ditlevsen, Susanne & Löcherbach, Eva, 2017. "Multi-class oscillating systems of interacting neurons," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1840-1869.
    5. Harin, Alexander, 2018. "Inequalities and zones. New mathematical results for behavioral and social sciences," MPRA Paper 90326, University Library of Munich, Germany.
    6. Alexander Harin, 2022. "Forbidden Zones for the Expectations of Data: New Mathematical Methods and Models for Behavioral Economics," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 8(1), pages 12-26, 12-2021.
    7. Harin, Alexander, 2021. "Behavioral economics. Forbidden zones. New method and models," MPRA Paper 106545, University Library of Munich, Germany.
    8. Harin, Alexander, 2020. "Behavioral sciences and auto-transformations of functions," MPRA Paper 99286, University Library of Munich, Germany.
    9. Harin, Alexander, 2019. "Behavioral sciences and auto-transformations. Introduction," MPRA Paper 97344, University Library of Munich, Germany.

    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:20:y:1985:i:2:p:323-331. 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.