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

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

Journal

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

Output data

Year: 2011, Volume: 52, Number: 5, Pages: 824-835 Pages count : 12 DOI: 10.1134/s0037446611050077

Tags

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

Authors

Dzhulaĭ N.A. ¹ , Kachurovskĭ A.G. ²

Affiliations

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
Elibrary:	18011620
OpenAlex:	W2010629454

DB	Citing
Web of science	9
Scopus	10
Elibrary	9
OpenAlex	12