On the rate of convergence in von Neumann's ergodic theorem with continuous time Full article
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Sbornik Mathematics
ISSN: 1064-5616 , E-ISSN: 1468-4802 |
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| Output data | Year: 2010, Volume: 201, Number: 4, Pages: 493-500 Pages count : 8 DOI: 10.1070/sm2010v201n04abeh004080 | ||||
| Tags | Rate of convergence of ergodic averages; Spectral measures of a dynamical system; Von Neumann's mean ergodic theorem; Wide-sense stationary stochastic processes | ||||
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Abstract:
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.
Cite:
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
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
Original:
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
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
Identifiers:
| Web of science: | WOS:000279452200007 |
| Scopus: | 2-s2.0-77954787013 |
| Elibrary: | 15316196 |
| OpenAlex: | W2056945163 |