仿射周期解是动力系统领域中一类新的研究对象，仿射周期性从时空对称角度给出一种新的周期性。考虑到某些动力学现象，其运动规律在时间上具有一种近似周期的概周期性，同时在空间上又呈现某种仿射对称性，本项目在仿射周期理论基础上，从时空角度提出一种新的概周期性，即仿射概周期性。.本项目以随机仿射概周期系统为研究对象，探究其在分布意义下的仿射概周期解的适定性。首先，拟采用不动点方法，利用新的收敛工具研究系统仿射概周期解的存在唯一性。其次，拟分别利用随机分离和半分离方法，研究线性与非线性随机微分方程仿射概周期解的存在性，给出随机仿射概周期情形下的分离与半分离条件。同时，利用Lyapunov函数法研究系统仿射概周期解的渐近稳定性，得到易于验证系统存在唯一渐近稳定的仿射概周期解的理论判据。我们期望建立一套框架性的方法研究随机微分方程仿射概周期解的适定性问题，并进一步拓展仿射概周期理论在随机微分方程领域的应用。

Affine-periodic solution is a new research topic in the field of dynamical systems. Affine periodicity gives a new periodicity from the perspective of space-time symmetry. Base on the theory of affine periodicity, we consider that the laws of motion for some dynamical phenomena exhibit almost periodicity in time and affine symmetry in space. We propose a new kind of almost periodicity from the perspective of space-time which is called affine-almost periodicity.. In this project, we take stochastic affine-almost periodic systems as the research object to study the well-posedness of affine-almost periodic solutions in distribution for the stochastic systems. Firstly, we study the existence and uniqueness of affine-almost periodic solutions of the stochastic systems by using the fixed point method and the new convergence tool. Secondly, the existence of affine-almost periodic solutions of linear and nonlinear stochastic differential equations is studied by using stochastic separation and semi-separation methods respectively. The stochastic separation and semi-separation conditions for stochastic almost periodic cases are given. Moreover, Lyapunov function method is used to study the asymptotic stability of affine-almost periodic solutions of the stochastic systems. The theoretical criterion to verify the existence, uniqueness and asymptotic stability of affine-almost periodic solutions is given. Through the research on this subject, we expected that a framework of method to study the well-posedness of affine-almost periodic solutions in distribution for stochastic differential equation can be established. At the same time, the scientific research can extend the application of the theory of affine-almost periodic solutions in the field of stochastic differential equations.