This paper is devoted to exponential stability of a class of non-autonomous stochastic differential equations with Markovian switching. By making use the time inhomogeneous property of the drift and diffusion coefficients, we derive sufficient and verifiable conditions for moment exponential stability and almost sure exponential stability. The contribution of the Markovian switching and time-inhomogeneous property to the stability is revealed. Two examples are provided to illustrate the effectiveness of our criteria.

中文翻译：

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具有马尔可夫切换的非自治随机微分方程的指数稳定性

本文致力于研究一类具有马尔可夫切换的非自治随机微分方程的指数稳定性。利用漂移系数和扩散系数的时间不均匀性，我们推导出矩指数稳定性和几乎确定指数稳定性的充分且可验证的条件。揭示了马尔可夫切换和时间非均匀性对稳定性的贡献。提供了两个例子来说明我们标准的有效性。