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

2024/01/16 by Dolgopyat, Dmitry, Hafouta, Yeor · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/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=∑_j=0^n-1f_j∘ T_j-1∘⋯∘ T₁∘ T₀ 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 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).

Cited by

• Limit theorems for inhomogeneous random walks on GL(d,\mathbb R)

Related

• Local limit theorems for expanding maps
• The almost sure invariance principle for unbounded functions of expanding maps
• Almost Sure Central Limit Theorems and the Erdos-Renyi law for Expanding Maps of the Interval
• A Berry-Esseen bound with (almost) sharp dependence conditions
• Berry-Esseen theorem and local limit theorem for non uniformly expanding maps