Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On stochastic Langevin and Fokker-Planck equations: the two-dimensional
  case   We prove existence, regularity in H\"older classes and estimates from above
and below of the fundamental solution of the stochastic Langevin equation. This
degenerate SPDE satisfies the weak H\"ormander condition. We use a Wentzell's
transform to reduce the SPDE to a PDE with random coefficients; then we apply a
new method, based on the parametrix technique, to construct a fundamental
solution. This approach avoids the use of the Duhamel's principle for the SPDE
and the related measurability issues that appear in the stochastic framework.
Our results are new even for the deterministic equation.

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The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
18
The categories of this paper are: econ