Constants in estimates for the rates of convergence in von Neumann's and Birkhoff's ergodic theorems | Sciact - Система учета научной деятельности ИМ СО РАН

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

Журнал

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

Вых. Данные

Год: 2011, Том: 202, Номер: 8, Страницы: 1105-1125 Страниц : 21 DOI: 10.1070/sm2011v202n08abeh004180

Ключевые слова

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

Авторы

Kachurovskii Alexander G ¹ , Sedalishchev Vladimir V ²

Организации

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 MathNet OpenAlex

Web of science:	WOS:000296354800002
Scopus:	2-s2.0-80054697774
РИНЦ:	18009586
OpenAlex:	W2040404163

БД	Цитирований
Web of science	17
Scopus	17
РИНЦ	16
OpenAlex	15