Periodic solutions of Fokker-Planck equations

In this paper, the existence of periodic solutions of Fokker-Planck equations is obtained by discussing the existence of periodic solutions in distribution for some stochastic differential equations. To prove the existence of periodic solutions in distribution for stochastic differential equations, a new criterion analogous to Halanay's criterion is given. Actually, the criterion is similar to a law of large numbers. Based on this criterion, the existence of periodic solutions in distribution for stochastic (functional) differential equations is established by Lyapunov's method.