Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ito formula for mild solutions of SPDEs with Gaussian and non-Gaussian
  noise and applications to stability properties   We use Yosida approximation to find an It\^o formula for mild solutions
$\left\{X^x(t), t\geq 0\right\}$ of SPDEs with Gaussian and non-Gaussian
coloured noise, the non Gaussian noise being defined through compensated
Poisson random measure associated to a L\'evy process. The functions to which
we apply such It\^o formula are in $C^{1,2}([0,T]\times H)$, as in the case
considered for SDEs in [9]. Using this It\^o formula we prove exponential
stability and exponential ultimate boundedness properties in mean square sense
for mild solutions. We also compare such It\^o formula to an It\^o formula for
mild solutions introduced by Ichikawa in [8], and an It\^o formula written in
terms of the semigroup of the drift operator [11] which we extend before to the
non Gaussian case.

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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph