In this paper, we consider the Bohl–Perron Theorem for linear random dynamical systems. We prove that the tempered exponential stability of a linear co-cycle is equivalent to the boundedness of solutions for inherit difference equation. Paper also proves a similar concept for co-cycle admitting a tempered exponential dichotomy.

中文翻译：

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随机动力系统的 Bohl–Perron 定理

在本文中，我们考虑线性随机动力系统的 Bohl-Perron 定理。我们证明线性余环的缓和指数稳定性等价于继承差分方程解的有界性。论文还证明了一个类似的概念，即承认缓和指数二分法的共循环。