Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transformations of infinitely divisible distributions via improper
  stochastic integrals   Let $X^{(\mu)}(ds)$ be an $\mathbb{R}^d$-valued homogeneous independently
scattered random measure over $\mathbb{R}$ having $\mu$ as the distribution of
$X^{(\mu)}((t,t+1])$. Let $f(s)$ be a nonrandom measurable function on an open
interval $(a,b)$ where $-\infty\leqslant a<b\leqslant\infty$. The improper
stochastic integral $\int_{a+}^{b-} f(s)X^{(\mu)}(ds)$ is studied. Its
distribution $\Phi_f(\mu)$ defines a mapping from $\mu$ to an infinitely
divisible distribution on $\mathbb{R}^d$. Three modifications (compensated,
essential, and symmetrized) and absolute definability are considered. After
their domains are characterized, necessary and sufficient conditions for the
domains to be very large (or very small) in various senses are given. The
concept of the dual in the class of purely non-Gaussian infinitely divisible
distributions on $\mathbb{R}^d$ is introduced and employed in studying some
examples. The $\tau$-measure $\tau$ of function $f$ is introduced and whether
$\tau$ determines $\Phi_f$ is discussed. Related transformations of L\'evy
measures are also studied.

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The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat