Moment bounds for a class of fractional stochastic heat equations
Foondun, Mohammud and Liu, Wei and Omaba, McSylvester (2014) Moment bounds for a class of fractional stochastic heat equations. Annals of Probability. pp. 124. ISSN 00911798 (In Press)

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Abstract
We consider fractional stochastic heat equations of the form $\frac{\partial u_t(x)}{\partial t} = (\Delta)^{\alpha/2} u_t(x)+\lambda \sigma (u_t(x)) \dot F(t,\, x)$. Here $\dot F$ denotes the noise term. Under suitable assumptions, we show that the second moment of the solution grows exponentially with time. In particular, this answers an open problem in \cite{CoKh}. Along the way, we prove a number of other interesting properties which extend and complement results in \cite{foonjose}, \cite{Khoshnevisan:2013aa} and \cite{Khoshnevisan:2013ab}.
Author(s):  Foondun, Mohammud, Liu, Wei and Omaba, McSylvester 

Item type:  Article 
ID code:  59235 
Keywords:  intermittence, stochastic partial differential equations, Probabilities. Mathematical statistics, Statistics and Probability 
Subjects:  Science > Mathematics > Probabilities. Mathematical statistics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Pure Administrator 
Date deposited:  22 Dec 2016 10:14 
Last modified:  08 Jan 2020 23:50 
URI:  https://strathprints.strath.ac.uk/id/eprint/59235 
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