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.

中文翻译：

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通过上下解决方案定期解决SDE

我们研究一种比Kolmogorov更好的递归：周期性递归，它对应于随机微分方程分布中的周期解。在上下解技术和比较原理的基础上，我们获得了随机微分方程（SDE）分布中周期解的存在性。因此，这为分析随机系统的周期性提供了一种有效的方法来研究其周期性。我们还将说明我们的结果。