Large-time behavior of non-symmetric FokkerPlanck 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. We dedicate this paper to Len Gross on the occasion of his 75th birthday. 1