IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2006-18.html
   My bibliography  Save this paper

Stochastic Nonlinear Schrödinger Equations Driven by a Fractional Noise Well Posedness, Large Deviations and Support

Author

Listed:
  • Eric Gautier

    (Crest)

Abstract

We consider stochastic nonlinear Schr¨odinger equations driven byan additive noise. The noise is fractional in time with Hurst parameter H in(0, 1). It is also colored in space and the space correlation operator is assumed tobe nuclear. We study the local well-posedness of the equation. Under adequateassumptions on the initial data, the space correlations of the noise and for somesaturated nonlinearities, we prove a sample path large deviations principle and asupport result. These results are stated in a space of exploding paths which areH¨older continuous in time until blow-up. We treat the case of Kerr nonlinearitieswhen H > 12 .

Suggested Citation

  • Eric Gautier, 2006. "Stochastic Nonlinear Schrödinger Equations Driven by a Fractional Noise Well Posedness, Large Deviations and Support," Working Papers 2006-18, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2006-18
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2006-18.pdf
    File Function: Crest working paper version
    Download Restriction: no
    ---><---

    More about this item

    Statistics

    Access and download statistics

    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:crs:wpaper:2006-18. 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: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.html .

    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.