This paper is concerned with the tempered exponential dichotomy for random differential systems in Banach spaces. Based on the presentation of bounded solutions for a tempered exponential dichotomous system, we give a bound under which the tempered exponentially dichotomous property of perturbed systems is preserved. Some applications of our results to stochastic partial differential equations are considered.

中文翻译：

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线性随机演化方程的缓和指数二分法

本文关注 Banach 空间中随机微分系统的调和指数二分法。基于调和指数二分系统的有界解的介绍，我们给出了一个界限，在该界限下，扰动系统的调和指数二分性质得以保留。考虑了我们的结果在随机偏微分方程中的一些应用。