Correlations and Convergence Rates in General Ergodic Theorems

Correlations and Convergence Rates in General Ergodic Theorems Full article

Journal

Theory of Probability and its Applications
ISSN: 0040-585X , E-ISSN: 1095-7219

Output data

Year: 2026, Volume: 70, Number: 4, Pages: 548-562 Pages count : 15 DOI: 10.1137/s0040585x97t992604

Authors

Kachurovskii A.G. ¹ , Podvigin I.V. ¹ , Todikov V.È. ¹

Affiliations

1	Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

In the ergodic theorem for unitary actions of Hausdorff locally compact second-countable groups, a formula is obtained for calculation of the norms of deviations of ergodic averages from their limit using known correlations. Illustrative examples are given. We also examine the inverse problem for recovery of sums of some sets of correlations from the known values of the norms of these deviations.

Kachurovskii A.G. , Podvigin I.V. , Todikov V.È.
Correlations and Convergence Rates in General Ergodic Theorems
Theory of Probability and its Applications. 2026. V.70. N4. P.548-562. DOI: 10.1137/s0040585x97t992604 Scopus OpenAlex

Качуровский А.Г. , Подвигин И.В. , Тодиков В.Э.
Корреляции и скорости сходимости в общих эргодических теоремах
Теория вероятностей и ее применения. 2025. Т.70. №4. С.672–689. DOI: 10.4213/tvp5837 РИНЦ OpenAlex MathNet

Published print:	Feb 20, 2026
Published online:	Feb 20, 2026

≡ Scopus:	2-s2.0-105031497580
≡ OpenAlex:	W7130539624