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Title: On some properties of a class of fractional stochastic heat equations
Authors: Liu, Wei
Tian, Kuanhou
Foondun, Mohammud
Keywords: Stochastic partial differential equations
Fractional Laplacian
Stochastic heat equation
Heat kernal
Issue Date: 2017
Publisher: Springer / © The Authors
Citation: LIU, W., TIAN, K. and FOONDUN, M., 2017. On some properties of a class of fractional stochastic heat equations. Journal of Theoretical Probability, 30(4), pp.1310-1333.
Abstract: We consider nonlinear parabolic stochastic equations of the form ∂tu = Lu + λσ(u) ˙ξ on the ball B(0, R), where ˙ξ denotes some Gaussian noise and σ is Lipschitz continuous. Here L corresponds to a symmetric α-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 σ, 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).
Description: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor: Research supported in part by EPSRC.
Version: Published
DOI: 10.1007/s10959-016-0684-6
URI: https://dspace.lboro.ac.uk/2134/21686
Publisher Link: http://dx.doi.org/10.1007/s10959-016-0684-6
ISSN: 0894-9840
Appears in Collections:Published Articles (Maths)

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