Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moment bounds for a class of fractional stochastic heat equations   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}.

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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas