Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The ergodic problem for some subelliptic operators with unbounded
  coefficients   We study existence and uniqueness of the invariant measure for a stochastic
process with degenerate diffusion, whose infinitesimal generator is a linear
subelliptic operator in the whole space R N with coefficients that may be
unbounded. Such a measure together with a Liouville-type theorem will play a
crucial role in two applications: the ergodic problem studied through
stationary problems with vanishing discount and the long time behavior of the
solution to a parabolic Cauchy problem. In both cases, the constants will be
characterized in terms of the invariant measure.

9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn