Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Coupling Property and the Liouville Theorem for
  Ornstein-Uhlenbeck Processes   Using a coupling for the weighted sum of independent random variables and the
explicit expression of the transition semigroup of Ornstein-Uhlenbeck processes
driven by compound Poisson processes, we establish the existence of a
successful coupling and the Liouville theorem for general Ornstein-Uhlenbeck
processes. Then we present the explicit coupling property of Ornstein-Uhlenbeck
processes directly from the behaviour of the corresponding symbol or
characteristic exponent. This approach allows us to derive gradient estimates
for Ornstein-Uhlenbeck processes via the symbol.

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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: eess