IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v127y2017i7p2316-2338.html
   My bibliography  Save this article

Intermittency for the Hyperbolic Anderson Model with rough noise in space

Author

Listed:
  • Balan, Raluca M.
  • Jolis, Maria
  • Quer-Sardanyons, Lluís

Abstract

In this article, we consider the stochastic wave equation on the real line driven by a linear multiplicative Gaussian noise, which is white in time and whose spatial correlation corresponds to that of a fractional Brownian motion with Hurst index H∈(14,12). Initial data are assumed to be constant. First, we prove that this equation has a unique solution (in the Skorohod sense) and obtain an exponential upper bound for the p-th moment the solution, for any p≥2. Condition H>14 turns out to be necessary for the existence of solution. Secondly, we show that this solution coincides with the one obtained by the authors in a recent publication, in which the solution is interpreted in the Itô sense. Finally, we prove that the solution of the equation in the Skorohod sense is weakly intermittent.

Suggested Citation

  • Balan, Raluca M. & Jolis, Maria & Quer-Sardanyons, Lluís, 2017. "Intermittency for the Hyperbolic Anderson Model with rough noise in space," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2316-2338.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:7:p:2316-2338
    DOI: 10.1016/j.spa.2016.10.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414916301971
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2016.10.009?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. Giordano, Luca M. & Jolis, Maria & Quer-Sardanyons, Lluís, 2020. "SPDEs with linear multiplicative fractional noise: Continuity in law with respect to the Hurst index," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7396-7430.
    2. Guerngar, Ngartelbaye & Nane, Erkan, 2020. "Moment bounds of a class of stochastic heat equations driven by space–time colored noise in bounded domains," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6246-6270.

    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:127:y:2017:i:7:p:2316-2338. 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.