  We study a kind of better recurrence than Kolmogorov's one: periodicity
recurrence,which corresponds periodic solutions in distribution for stochastic
differential equations. On the basis of technique of upper and lower solutions
and comparison principle, we obtain the existence of periodic solutions in
distribution for stochastic differential equations (SDEs). Hence this provides
an effective method how to study the periodicity of stochastic systems by
analyzing deterministic ones. We also illustrate our results.
