Large Deviations of the Ergodic Averages: From Hölder Continuity to Continuity Almost Everywhere

Large Deviations of the Ergodic Averages: From Hölder Continuity to Continuity Almost Everywhere Full article

Journal

Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126

Output data

Year: 2018, Volume: 28, Number: 1, Pages: 23-38 Pages count : 16 DOI: 10.3103/s1055134418010029

Tags

Birkhoff’s ergodic theorem; large deviations; Pomeau–Manneville mapping; rates of convergence in ergodic theorems; return time

Authors

Kachurovskiĭ A.G. ^1,2 , Podvigin I.V. ^1,2

Affiliations

1	Sobolev Institute of Mathematics
2	Novosibirsk State University

For many dynamical systems that are popular in applications, estimates are known for the decay of large deviations of the ergodic averages in the case of Hölder continuous averaging functions. In the present article, we show that these estimates are valid with the same asymptotics in the case of bounded almost everywhere continuous functions. Using this fact, we obtain, in the case of such functions, estimates for the rate of convergence in Birkhoff’s ergodic theorem and for the distribution of the time of return to a subset of the phase space.

Kachurovskiĭ A.G. , Podvigin I.V.
Large Deviations of the Ergodic Averages: From Hölder Continuity to Continuity Almost Everywhere
Siberian Advances in Mathematics. 2018. V.28. N1. P.23-38. DOI: 10.3103/s1055134418010029 Scopus РИНЦ OpenAlex

Качуровский А.Г. , Подвигин И.В.
Большие уклонения эргодических средних: переход от гёльдеровости к непрерывности почти всюду
Математические труды. 2017. Т.20. №1. С.97-120. DOI: 10.17377/mattrudy.2017.20.106 РИНЦ MathNet

Scopus:	2-s2.0-85043507663
Elibrary:	35498415
OpenAlex:	W2794147199

DB	Citing
Scopus	3
Elibrary	3
OpenAlex	3