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}.


Item type: Article ID code: 59235 Dates: DateEvent19 September 2014Published19 September 2014AcceptedKeywords: 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: 01 Nov 2023 10:46 URI: https://strathprints.strath.ac.uk/id/eprint/59235