On the constants in the estimates of the rate of convergence in von Neumann's ergodic theorem

被引：7

作者：

Kachurovskii, A. G. ^{[1
]}

Sedalishchev, V. V. ^{[2
]}

机构：

[1] Russian Acad Sci, Sobolev Inst Math, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, Novosibirsk 630090, Russia

来源：

MATHEMATICAL NOTES | 2010年 / 87卷 / 5-6期

关键词：

von Neumann's ergodic theorem; ergodic mean; spectral measure; dynamical system; wide-sense stationary stochastic process; correlation coefficient; Darboux sum;

D O I：

10.1134/S000143461005010X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the rate of convergence in von Neumann's ergodic theorem. We obtain constants connecting the power rate of convergence of ergodic means and the power singularity at zero of the spectral measure of the corresponding dynamical system (these concepts are equivalent to each other). All the results of the paper have obvious exact analogs for wide-sense stationary stochastic processes.

引用

页码：720 / 727

页数：8

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