Rates of convergence in CLT and ASIP for sequences of expanding maps

Dmitry Dolgopyat; Yeor Hafouta

paper

Rates of convergence in CLT and ASIP for sequences of expanding maps

arXiv:2401.08802

Abstract

We prove Berry-Esseen theorems and the almost sure invariance principle with rates for partial sums of the form $S_{n} = \sum_{j = 0}^{n - 1} f_{j} \circ T_{j - 1} \circ \dots \circ T_{1} \circ T_{0}$ where $f_{j}$ are functions with uniformly bounded ``variation" and $T_{j}$ is a sequence of expanding maps. Using symbolic representations similar result follow for maps $T_{j}$ in a small $C^{1}$ neighborhood of an Axiom A map and Hölder continuous functions $f_{j}$ . All of our results are already new for a single map $T_{j} = T$ and a sequence of different functions $(f_{j})$ .