In this paper, we aim to study a stochastic process from a macro point of view, and thus, periodic solution of a stochastic process in distributional sense is introduced. We first give the definition and then establish the existence of periodic solution on bounded domain. Lastly, for the case that probability density function exists, we obtain the existence periodic solutions of the probability density function corresponding to the stochastic process by using the technique of deterministic partial differential equations.

中文翻译：

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分布意义上的随机过程的周期解

本文旨在从宏观的角度研究随机过程，从而介绍了分布意义上的随机过程的周期解。我们首先给出定义，然后确定有界域上周期解的存在性。最后，针对存在概率密度函数的情况，利用确定性偏微分方程技术，获得了与随机过程相对应的概率密度函数的存在周期解。