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

Constants in the estimates of the rate of convergence in von Neumann’s ergodic theorem with continuous time Научная публикация

Журнал

Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260

Вых. Данные

Год: 2011, Том: 52, Номер: 5, Страницы: 824-835 Страниц : 12 DOI: 10.1134/s0037446611050077

Ключевые слова

correlation function; rate of convergence of ergodic averages; spectral measure; stationary stochastic process; von Neumann mean ergodic theorem

Авторы

Dzhulaĭ N.A. ¹ , Kachurovskĭ A.G. ²

Организации

1	Novosibirsk State University
2	Sobolev Institute of Mathematics

Estimates for the rate of convergence in ergodic theorems are necessarily spectral. We find the equivalence constants relating the polynomial rate of convergence in von Neumann's mean ergodic theorem with continuous time and the polynomial singularity at the origin of the spectral measure of the function averaged over the corresponding dynamical system. We also estimate the same rate of convergence with respect to the decrease rate of the correlation function. All results of this article have obvious exact analogs for the stochastic processes stationary in the wide sense.

Dzhulaĭ N.A. , Kachurovskĭ A.G.
Constants in the estimates of the rate of convergence in von Neumann’s ergodic theorem with continuous time
Siberian Mathematical Journal. 2011. V.52. N5. P.824-835. DOI: 10.1134/s0037446611050077 WOS Scopus РИНЦ OpenAlex

Джулай Н.А. , Качуровский А.Г.
Константы оценок скорости сходимости в эргодической теореме фон Неймана с непрерывным временем
Сибирский математический журнал. 2011. Т.52. №5. С.1039-1052. РИНЦ MathNet

Web of science:	WOS:000298650500007
Scopus:	2-s2.0-80155151869
РИНЦ:	18011620
OpenAlex:	W2010629454

БД	Цитирований
Web of science	9
Scopus	10
РИНЦ	9
OpenAlex	12