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On some properties of a class of fractional stochastic heat equations

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journal contribution
posted on 16.06.2016 by Wei Liu, Kuanhou Tian, Mohammud Foondun
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).

Funding

Research supported in part by EPSRC.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Theoretical Probability

Pages

1 - 24

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.

Publisher

Springer / © The Authors

Version

VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/ by/4.0/

Publication date

2017

Notes

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.

ISSN

0894-9840

eISSN

1572-9230

Language

en

Licence

Exports