2000 character limit reached
Rates of convergence in CLT and ASIP for sequences of expanding maps (2401.08802v1)
Published 16 Jan 2024 in math.DS and math.PR
Abstract: We prove Berry-Esseen theorems and the almost sure invariance principle with rates for partial sums of the form $S_n=\sum_{j=0}{n-1}f_j\circ T_{j-1}\circ\cdots\circ T_1\circ T_0$ 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 $C1$ neighborhood of an Axiom A map and H\"older continuous functions $f_j$. All of our results are already new for a single map $T_j=T$ and a sequence of different functions $(f_j)$.
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