Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Skorohod spaces as universal sample path spaces   The paper presents a factorization theorem for a certain class of stochastic
processes. Skorohod spaces carry the rich structure of standard Borel spaces
and appear to be suitable universal sample path spaces. We show that, if $\xi$
is a RCLL stochastic process with values in a complete separable metric space
$E$, any other RCLL stochastic process $X$ adapted to the filtration induced by
$\xi$ factors through the Skorohod space $D_E[0,\infty)$. This can be
understood as an extension of a stochastic process to a standard Borel space
enjoying nice properties. Moreover, the trajectories of the factorized
stochastic process defined on $D_E[0,\infty)$ inherit the properties of being
continuous, non-decreasing, and of bounded variation, resp., from those of $X$.
  Considering situations which are invariant under the factorization procedure,
the main theorem is a reduction tool to assume the underlying measurable space
be a standard Borel space. In an example, we pick the existence theorem of
regular conditional probabilities on standard Borel spaces to simplify a
conditional expectation appearing in stochastic control problems.

9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
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The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio