IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v196y2023ics0167715223000317.html
   My bibliography  Save this article

On a class of mixed stochastic heat equations driven by spatially homogeneous Gaussian noise

Author

Listed:
  • Zhang, Bin
  • Yao, Zhigang
  • Liu, Junfeng

Abstract

In this paper, we study a class of nonlinear stochastic heat equations ∂∂tu(t,x)=Δ+aαΔα2+b⋅∇u(t,x)+σ(u(t,x))Ẇ(t,x), where Ẇ denotes the Gaussian noise which is white in time and spatially homogeneous in space. The existence, uniqueness and the Hölder continuity of the mild solution to the above equation are proved.

Suggested Citation

  • Zhang, Bin & Yao, Zhigang & Liu, Junfeng, 2023. "On a class of mixed stochastic heat equations driven by spatially homogeneous Gaussian noise," Statistics & Probability Letters, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:stapro:v:196:y:2023:i:c:s0167715223000317
    DOI: 10.1016/j.spl.2023.109807
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715223000317
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2023.109807?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.

    References listed on IDEAS

    as
    1. Hu, Yaozhong & Nualart, David & Song, Jian, 2013. "A nonlinear stochastic heat equation: Hölder continuity and smoothness of the density of the solution," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1083-1103.
    2. Raluca M. Balan & Ciprian A. Tudor, 2010. "Stochastic Heat Equation with Multiplicative Fractional-Colored Noise," Journal of Theoretical Probability, Springer, vol. 23(3), pages 834-870, September.
    3. Chen, Zhen-Qing & Hu, Eryan, 2015. "Heat kernel estimates for Δ+Δα/2 under gradient perturbation," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2603-2642.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    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. Chen, Xin & Chen, Zhen-Qing & Wang, Jian, 2020. "Heat kernel for non-local operators with variable order," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3574-3647.
    2. Li, Kexue, 2017. "Hölder continuity for stochastic fractional heat equation with colored noise," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 34-41.
    3. Hu, Yaozhong & Li, Juan & Mi, Chao, 2023. "BSDEs generated by fractional space-time noise and related SPDEs," Applied Mathematics and Computation, Elsevier, vol. 450(C).

    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:stapro:v:196:y:2023:i:c:s0167715223000317. 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/622892/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.