We prove comparison theorems for stochastic differential equations (briefly, SDE) with respect to a standard multidimensional Wiener process as well as for components of systems of SDE with respect to a multidimensional Wiener process. The obtained results are applied to the study of the stability with probability 1 of the perturbed solutions to the SDE.

中文翻译：

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随机微分方程组的稳定性和比较定理

我们证明了相对于标准多维维纳过程的随机微分方程（简称SDE）以及相对于多维维纳过程的SDE系统组件的比较定理。所得结果用于SDE摄动解的概率为1的稳定性研究。