On the rate of convergence in von Neumann's ergodic theorem with continuous time | Sciact - Система учета научной деятельности ИМ СО РАН

On the rate of convergence in von Neumann's ergodic theorem with continuous time Научная публикация

Журнал

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

Вых. Данные

Год: 2010, Том: 201, Номер: 4, Страницы: 493-500 Страниц : 8 DOI: 10.1070/sm2010v201n04abeh004080

Ключевые слова

Rate of convergence of ergodic averages; Spectral measures of a dynamical system; Von Neumann's mean ergodic theorem; Wide-sense stationary stochastic processes

Авторы

Kachurovskii A G ¹ , Reshetenko Anna V ²

Организации

1	Sobolev Institute of Mathematics
2	Novosibirsk State University

The rate of convergence in von Neumann’s mean ergodic theorem is studied for continuous time. The condition that the rate of convergence of the ergodic averages be of power-law type is shown to be equivalent to requiring that the spectral measure of the corresponding dynamical system have a power-type singularity at 0. This forces the estimates for the convergence rate in the above ergodic theorem to be necessarily spectral. All the results obtained have obvious exact analogues for wide-sense stationary processes.

Kachurovskii A.G. , Reshetenko A.V.
On the rate of convergence in von Neumann's ergodic theorem with continuous time
Sbornik Mathematics. 2010. V.201. N4. P.493-500. DOI: 10.1070/sm2010v201n04abeh004080 WOS Scopus РИНЦ OpenAlex

Качуровский А.Г. , Решетенко А.В.
О скорости сходимости в эргодической теореме фон Неймана с непрерывным временем
Математический сборник. 2010. Т.201. №4. С.25-32. DOI: 10.4213/sm7622 РИНЦ MathNet OpenAlex

Web of science:	WOS:000279452200007
Scopus:	2-s2.0-77954787013
РИНЦ:	15316196
OpenAlex:	W2056945163

БД	Цитирований
Web of science	9
Scopus	10
РИНЦ	11
OpenAlex	14