Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Stein's Method for Infinitely Divisible Laws With Finite First Moment   We present, in a unified way, a Stein methodology for infinitely divisible
laws (without Gaussian component) having finite first moment. Based on a
correlation representation, we obtain a characterizing non-local Stein operator
which boils down to classical Stein operators in specific examples. Thanks to
this characterizing operator, we introduce various extensions of size bias and
zero bias distributions and prove that these notions are closely linked to
infinite divisibility. Combined with standard Fourier techniques, these
extensions also allow obtaining explicit rates of convergence for compound
Poisson approximation in particular towards the symmetric $\alpha$-stable
distribution. Finally, in the setting of non-degenerate self-decomposable laws,
by semigroup techniques, we solve the Stein equation induced by the
characterizing non-local Stein operator and obtain quantitative bounds in weak
limit theorems for sums of independent random variables going back to the work
of Khintchine and L\'evy.

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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: physics