A. Arnold, E. Carlen, Q. Ju:

"Large-time behavior of non-symmetric Fokker-Planck type equations";

in: "ASC Report09/2008", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2008, ISBN: 978-3-902627-01-8.

Large time asymptotics of the solutions to non-symmetric Fokker-

Planck type equations are studied by extending the entropy method to this

case. We present a modified Bakry-Emery criterion that yields covergence of

the solution to the steady state in relative entropy with an explicit exponen-

tial rate. In parallel it also implies a logarithmic Sobolev inequality w.r.t. the

steady state measure. Explicit examples illustrate that skew-symmetric per-

turbations in the Fokker Planck operator can "help" to improve the constant

in such a logarithmic Sobolev inequality.

http://www.asc.tuwien.ac.at/preprint/2008/asc09x2008.pdf

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