Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\Phi$-Entropy Inequality and Invariant Probability Measure for SDEs
  with Jump   By using the $\Phi$-entropy inequality derived in \cite{Wu, Ch} for Poisson
measures, the same type of inequality is established for a class of stochastic
differential equations driven by purely jump L\'evy processes. The semigroup
$\Phi$-entropy inequality for SDEs driven by Poisson point processes as well as
a sharp result on the existence of invariant probability measures are also
presented.

13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex