论文标题
动态系统的本地和中心限制定理的扩展
Expansions in the local and the central limit theorems for dynamical systems
论文作者
论文摘要
我们研究了Berry-Esséen估计值（Edgeworth扩展）和局部限制定理中的高阶扩展，用于保留动力学系统的混乱概率总和。我们在技术假设下建立一般结果，讨论这些假设的验证，并通过不同的示例（有限型，Young Towers，Sinai台球，随机矩阵产品的子缩短）来说明我们的结果，包括无界可观察性的情况，其可集成性顺序与I.I.D中所需的最佳时刻条件任意接近。环境。
We study higher order expansions both in the Berry-Esséen estimate (Edgeworth expansions) and in the local limit theorems for Birkhoff sums of chaotic probability preserving dynamical systems. We establish general results under technical assumptions, discuss the verification of these assumptions and illustrate our results by different examples (subshifts of finite type, Young towers, Sinai billiards, random matrix products), including situations of unbounded observables with integrability order arbitrarily close to the optimal moment condition required in the i.i.d. setting.
