In this paper, we establish a LaSalle-type stationary oscillation principle to obtain the existence and stability of affine periodic solutions in distribution for stochastic differential equations. As applications, we show the existence and asymptotic stability of stochastic affine periodic solutions in distribution via Lyapunov’s method.

中文翻译：

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随机仿射周期系统的 LaSalle 型稳态振荡原理

在本文中，我们建立了拉萨尔型平稳振荡原理来获得随机微分方程分布中仿射周期解的存在性和稳定性。作为应用，我们通过李亚普诺夫方法证明了分布中随机仿射周期解的存在性和渐近稳定性。