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

Abstract

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.