解的回复性是随机微分方程领域的一个重要的议题。作为一种弱于周期解的回复解，概周期解能更好地适应具有回复性的模型，因而在应用中具有重要意义。近年来，越来越多的研究者开始关注随机微分方程概周期问题。有关这个问题的许多结论基于两个基本假设：方程系数具有概周期性和存在均方有界解。于是产生一个问题：若去掉有界解存在的假设，能否得到具有较弱意义下概周期性，如几乎自守或Levitan概周期性的解？在前期工作中，申请人及合作者提出了随机分离或半分离方法以得到随机微分方程的依分布概周期解。本项目中我们拟采用这种方法，并借助Lyapunov第二方法，通过解的稳定性以及渐进性以保证不同的解彼此分离，从而解决这个问题。此外，我们考虑了弱概周期解在带有随机项的传染病动力学模型及Li二阶方程如Lienard方程中的应用。

Recurrence is an important thesis about stochastic differential equation (SDEs). As a kind of recurrence weaker than periodicity, almost periodic solutions simulate models better, hence it's useful in applications. In recent years, more and more researchers are concentrated on almost periodic problems of SDEs. Basing on the existence of mean square bounded solutions they've gained some results under an assumption of almost periodic coefficients. Then there's a nature problem: would the SDE admits some recurrent solutions with distribution almost periodic in weaker or general sense, such as almost automorphic or Levitan almost periodic? In our former works, we investigated a stochastic separating method to gain SDEs' solutions with almost periodic distribution. We choose this method to solve this problem, and separate different solutions via Lyapunov second method. Otherwise, we will use our theories to real models such as stochastic epidemic dynamical models and two order equations such as Lienard equation.