Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Stochastic Heat Equation with a Fractional-Colored Noise: Existence
  of the Solution   In this article we consider the stochastic heat equation $u_{t}-\Delta u=\dot
B$ in $(0,T) \times \bR^d$, with vanishing initial conditions, driven by a
Gaussian noise $\dot B$ which is fractional in time, with Hurst index $H \in
(1/2,1)$, and colored in space, with spatial covariance given by a function
$f$. Our main result gives the necessary and sufficient condition on $H$ for
the existence of the process solution. When $f$ is the Riesz kernel of order
$\alpha \in (0,d)$ this condition is $H>(d-\alpha)/4$, which is a relaxation of
the condition $H>d/4$ encountered when the noise $\dot B$ is white in space.
When $f$ is the Bessel kernel or the heat kernel, the condition remains
$H>d/4$.

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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cs