Rates in almost sure invariance principle for quickly mixing dynamical systems
Probability
2018-11-26 v1 Dynamical Systems
Abstract
For a large class of quickly mixing dynamical systems, we prove that the error in the almost sure approximation with a Brownian motion is of order O((log n)^a) with a 2. Specifically, we consider nonuniformly expanding maps with exponential and stretched exponential decay of correlations, with one-dimensional H{\"o}lder continuous observables.
Cite
@article{arxiv.1811.09094,
title = {Rates in almost sure invariance principle for quickly mixing dynamical systems},
author = {C Cuny and J Dedecker and A Korepanov and Florence Merlevède},
journal= {arXiv preprint arXiv:1811.09094},
year = {2018}
}