Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mild Solutions for a Class of Fractional SPDEs and Their Sample Paths   In this article we introduce and analyze a notion of mild solution for a
class of non-autonomous parabolic stochastic partial differential equations
defined on a bounded open subset $D\subset\mathbb{R}^{d}$ and driven by an
infinite-dimensional fractional noise. The noise is derived from an
$L^{2}(D)$-valued fractional Wiener process $W^{H}$ whose covariance operator
satisfies appropriate restrictions; moreover, the Hurst parameter $H$ is
subjected to constraints formulated in terms of $d$ and the H\"{o}lder exponent
of the derivative $h^\prime$ of the noise nonlinearity in the equations. We
prove the existence of such solution, establish its relation with the
variational solution introduced in \cite{nuavu} and also prove the H\"{o}lder
continuity of its sample paths when we consider it as an $L^{2}(D)$--valued
stochastic processes. When $h$ is an affine function, we also prove uniqueness.
The proofs are based on a relation between the notions of mild and variational
solution established in Sanz-Sol\'e and Vuillermot 2003, and adapted to our
problem, and on a fine analysis of the singularities of Green's function
associated with the class of parabolic problems we investigate. An immediate
consequence of our results is the indistinguishability of mild and variational
solutions in the case of uniqueness.

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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex