Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sufficient Conditions for Existence of $J_{\alpha}(X +
  \sqrt[\alpha]{\eta}N)$   In his technical report~\cite[sec. 6]{barrontech}, Barron states that the de
Bruijn's identity for Gaussian perturbations holds for any RV having a finite
variance. In this report, we follow Barron's steps as we prove the existence of
$J_{\alpha}\left(X + \sqrt[\alpha]{\eta}N\right)$, $\eta > 0$ for any Radom
Variable (RV) $X \in \mathcal{L}$ where \begin{equation*} \mathcal{L} = \left\{
\text{RVs} \,\,U: \int \ln\left(1 + |U|\right)\,dF_{U}(u) \text{ is finite }
\right\}, \end{equation*} and where $N \sim \mathcal{S}(\alpha;1)$ is
independent of $X$, $0< \alpha <2$.

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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom