不定常动力系统的一个中心极限定理
A central limit theorem for time-dependent dynamical systems
摘要：
该工作[8]确定了在区间均匀扩展映射的不定常（非随机）情况下的记忆丧失。在这里，我们找到的条件下，我们有收敛到正态分布的适当规模的Birkhoff样部分和适当的检验函数。问题的一个重要部分是要确保部分和的方差趋于无穷大（参见图1）。在自治情况下的零上同调条件）。实际上，本文是第一个非随机的，即。e.还发现了一些具体的例子，它们不是给定映射的小扰动。我们的方法使用鞅逼近技术的形式[9]。
英文摘要：
The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled Birkhoff-like partial sums of appropriate test functions. A substantial part of the problem is to ensure that the variances of the partial sums tend to infinity (cf. the zero-cohomology condition in the autonomous case). In fact, the present paper is the first one where non-random, i. e. specific examples are also found, which are not small perturbations of a given map. Our approach uses martingale approximation technique in the form of [9].
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