IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i11p3914-3938.html
   My bibliography  Save this article

Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations

Author

Listed:
  • Nualart, David
  • Quer-Sardanyons, Lluís

Abstract

In this paper we establish lower and upper Gaussian bounds for the solutions to the heat and wave equations driven by an additive Gaussian noise, using the techniques of Malliavin calculus and recent density estimates obtained by Nourdin and Viens in [17]. In particular, we deal with the one-dimensional stochastic heat equation in [0, 1] driven by the space-time white noise, and the stochastic heat and wave equations in (d>=1 and d

Suggested Citation

  • Nualart, David & Quer-Sardanyons, Lluís, 2009. "Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(11), pages 3914-3938, November.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:11:p:3914-3938
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(09)00152-5
    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. Márquez-Carreras, D. & Mellouk, M. & Sarrà, M., 2001. "On stochastic partial differential equations with spatially correlated noise: smoothness of the law," Stochastic Processes and their Applications, Elsevier, vol. 93(2), pages 269-284, June.
    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. Hildebrandt, Florian & Trabs, Mathias, 2023. "Nonparametric calibration for stochastic reaction–diffusion equations based on discrete observations," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 171-217.
    2. Junfeng Liu & Litan Yan, 2016. "Solving a Nonlinear Fractional Stochastic Partial Differential Equation with Fractional Noise," Journal of Theoretical Probability, Springer, vol. 29(1), pages 307-347, March.

    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. Ferrario, Benedetta & Zanella, Margherita, 2019. "Absolute continuity of the law for the two dimensional stochastic Navier–Stokes equations," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1568-1604.

    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:119:y:2009:i:11:p:3914-3938. 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.