Precise asymptotics on the Birkhoff sums for dynamical systems
Dynamical Systems
2021-10-27 v2 Probability
Abstract
We establish two precise asymptotic results on the Birkhoff sums for dynamical systems. These results are parallel to that on the arithmetic sums of independent and identically distributed random variables previously obtained by Hsu and Robbins, Erd\H{o}s, Heyde. We apply our results to the Gauss map and obtain new precise asymptotics in the theorem of L\'evy on the regular continued fraction expansion of irrational numbers in .
Cite
@article{arxiv.2012.05500,
title = {Precise asymptotics on the Birkhoff sums for dynamical systems},
author = {Lulu Fang and Hiroki Takahasi and Yiwei Zhang},
journal= {arXiv preprint arXiv:2012.05500},
year = {2021}
}