On some properties of a class of fractional stochastic heat equations

Wei Liu, Kuanhou Tian, Mohammud Foondun

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We consider nonlinear parabolic stochastic equations of the form ∂tu=Lu+λσ(u)ξ˙∂tu=Lu+λσ(u)ξ˙ on the ball B(0,R)B(0,R) , where ξ˙ξ˙ denotes some Gaussian noise and σσ is Lipschitz continuous. Here LL corresponds to a symmetric αα -stable process killed upon exiting B(0, R). We will consider two types of noises: space-time white noise and spatially correlated noise. Under a linear growth condition on σσ , we study growth properties of the second moment of the solutions. Our results are significant extensions of those in Foondun and Joseph (Stoch Process Appl, 2014) and complement those of Khoshnevisan and Kim (Proc AMS, 2013, Ann Probab, 2014).

Original languageEnglish
Number of pages24
JournalJournal of Theoretical Probability
Publication statusPublished - 19 May 2016


  • fractional laplacian
  • heat kernel
  • stochastic heat equation
  • stochastic partial differential equations

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