This paper mainly focuses on the stationary probability distribution of stochastic differential equations (SDEs) under regime switching. We give the explicit expression of stationary distribution according to the limit probability distribution of SDEs under some conditions. As a special case, we obtain the stationary distribution of SDEs with Markovian switching as the weighted mean of the stationary distribution of its subsystems. In the end, an example and some conclusions are given to illustrate our theoretical results of this paper.

中文翻译：

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状态切换下SDE非平凡平稳分布的显式表达

本文主要研究状态切换下随机微分方程（SDE）的平稳概率分布。在某些条件下，我们根据SDE的极限概率分布给出了平稳分布的明确表示。作为一种特殊情况，我们使用马尔可夫切换获得SDE的平稳分布作为其子系统平稳分布的加权平均值。最后给出一个例子和一些结论来说明本文的理论结果。