We present an adaptation of Stein’s method of normal approximation to the study of both discrete- and continuous-time dynamical systems. We obtain new correlation-decay conditions on dynamical systems for a multivariate central limit theorem augmented by a rate of convergence. We then present a scheme for checking these conditions in actual examples. The principal contribution of our paper is the method, which yields a convergence rate essentially with the same amount of work as the central limit theorem, together with a multiplicative constant that can be computed directly from the assumptions.

中文翻译：

---

动态系统的 Stein 法线逼近法

我们将 Stein 的正态逼近方法应用于离散时间和连续时间动态系统的研究。我们获得了动态系统上新的相关衰减条件，用于通过收敛速度增强的多元中心极限定理。然后，我们提出了一个在实际示例中检查这些条件的方案。我们论文的主要贡献是该方法，它产生的收敛速度基本上与中心极限定理具有相同的工作量，以及可以直接从假设中计算的乘法常数。