# 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. 1-24. ISSN 0091-1798 (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 59235 DateEvent19 September 2014Published19 September 2014Accepted intermittence, stochastic partial differential equations, Probabilities. Mathematical statistics, Statistics and Probability Science > Mathematics > Probabilities. Mathematical statistics Faculty of Science > Mathematics and Statistics Pure Administrator 22 Dec 2016 10:14 23 Jul 2021 01:26 https://strathprints.strath.ac.uk/id/eprint/59235