IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i10p6246-6270.html
   My bibliography  Save this article

Moment bounds of a class of stochastic heat equations driven by space–time colored noise in bounded domains

Author

Listed:
  • Guerngar, Ngartelbaye
  • Nane, Erkan

Abstract

We consider the fractional stochastic heat type equation ∂∂tut(x)=−(−Δ)α∕2ut(x)+ξσ(ut(x))Ḟ(t,x),x∈D,t>0,with nonnegative bounded initial condition, where α∈(0,2], ξ>0 is the noise level, σ:R→R is a globally Lipschitz function satisfying some growth conditions and the noise term Ḟ behaves in space like the Riez kernel and is possibly correlated in time and D is the unit open ball centered at the origin in Rd. When the noise term is not correlated in time, we establish a change in the growth of the solution of these equations depending on the noise level ξ. On the other hand when the noise term behaves in time like the fractional Brownian motion with index H∈(1∕2,1), We also derive explicit bounds leading to a well-known intermittency property.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:10:p:6246-6270
    DOI: 10.1016/j.spa.2020.05.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414920302714
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2020.05.009?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.

    References listed on IDEAS

    as
    1. Balan, Raluca M. & Conus, Daniel, 2014. "A note on intermittency for the fractional heat equation," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 6-14.
    2. Xie, Bin, 2016. "Some effects of the noise intensity upon non-linear stochastic heat equations on [0,1]," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1184-1205.
    3. Foondun, Mohammud & Guerngar, Ngartelbaye & Nane, Erkan, 2017. "Some properties of non-linear fractional stochastic heat equations on bounded domains," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 86-93.
    4. 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.
    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. Yan, Litan & Yu, Xianye & Sun, Xichao, 2016. "Asymptotic behavior of the solution of the fractional heat equation," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 54-61.
    2. Foondun, Mohammud & Guerngar, Ngartelbaye & Nane, Erkan, 2017. "Some properties of non-linear fractional stochastic heat equations on bounded domains," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 86-93.
    3. 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.
    4. Harin, Alexander, 2018. "Forbidden zones for the expectation. New mathematical results for behavioral and social sciences," MPRA Paper 86650, University Library of Munich, Germany.
    5. Song, Jian, 2017. "On a class of stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 37-79.
    6. Litan Yan & Xianye Yu, 2019. "Asymptotic Behavior for High Moments of the Fractional Heat Equation with Fractional Noise," Journal of Theoretical Probability, Springer, vol. 32(4), pages 1617-1646, December.

    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:eee:spapps:v:130:y:2020:i:10:p:6246-6270. 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.