Constants in estimates for the rates of convergence in von Neumann's and Birkhoff's ergodic theorems

Constants in estimates for the rates of convergence in von Neumann's and Birkhoff's ergodic theorems Full article

Journal

Sbornik Mathematics
ISSN: 1064-5616 , E-ISSN: 1468-4802

Output data

Year: 2011, Volume: 202, Number: 8, Pages: 1105-1125 Pages count : 21 DOI: 10.1070/sm2011v202n08abeh004180

Tags

Correlation coefficients; Rates of convergence in ergodic theorems; Spectral measures; Wide-sense stationary processes

Authors

Kachurovskii Alexander G ¹ , Sedalishchev Vladimir V ²

Affiliations

1	Sobolev Institute of Mathematics
2	Novosibirsk State University

The paper investigates estimates which relate two equivalent phenomena: the power-type rate of convergence in von Neumann's ergodic theorem and the power-type singularity at zero (with the same exponent) exhibited by the spectral measure of the function being averaged with respect to the corresponding dynamical system. The same rate of convergence is also estimated in terms of the rate of decrease of the correlation coefficients. Also, constants are found in analogous estimates for the power-type convergence in Birkhoff's ergodic theorem. All the results have exact analogues for wide-sense stationary stochastic processes.

Kachurovskii A.G. , Sedalishchev V.V.
Constants in estimates for the rates of convergence in von Neumann's and Birkhoff's ergodic theorems
Sbornik Mathematics. 2011. V.202. N8. P.1105-1125. DOI: 10.1070/sm2011v202n08abeh004180 WOS Scopus РИНЦ OpenAlex

Качуровский А.Г. , Седалищев В.В.
Константы оценок скорости сходимости в эргодических теоремах фон Неймана и Биркгофа
Математический сборник. 2011. Т.202. №8. С.21-40. DOI: 10.4213/sm7717 РИНЦ OpenAlex MathNet

≡ Web of science:	WOS:000296354800002
≡ Scopus:	2-s2.0-80054697774
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