Interrelation between the convergence rates in von Neumann’s and Birkhoff’s ergodic theorems Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2014, Volume: 55, Number: 2, Pages: 336-348 Pages count : 13 DOI: 10.1134/s0037446614020165 | ||
| Tags | von Neumann’s ergodic theorem, Birkhoff’s ergodic theorem, convergence rate of ergodic averages, wide-sense stationary stochastic process, contraction semigroups in Lp | ||
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Abstract:
In the L p spaces, 1 < p < ∞, we prove some inequalities for discrete and continuous times that make it possible to obtain the convergence rate in Birkhoff’s theorem in the presence of bounds on the convergence rate in von Neumann’s ergodic theorem belonging to a sufficiently large rate range. The exact operator analogs of these inequalities for contraction semigroups in L p are given. These results also have the obvious exact analogs in the class of wide-sense stationary stochastic processes.
Cite:
Sedalishchev V.V.
Interrelation between the convergence rates in von Neumann’s and Birkhoff’s ergodic theorems
Siberian Mathematical Journal. 2014. V.55. N2. P.336-348. DOI: 10.1134/s0037446614020165 WOS Scopus OpenAlex
Interrelation between the convergence rates in von Neumann’s and Birkhoff’s ergodic theorems
Siberian Mathematical Journal. 2014. V.55. N2. P.336-348. DOI: 10.1134/s0037446614020165 WOS Scopus OpenAlex
Dates:
| Submitted: | Jun 14, 2013 |
| Published print: | Apr 30, 2014 |
| Published online: | Apr 30, 2014 |
Identifiers:
| ≡ Web of science: | WOS:000335167300016 |
| ≡ Scopus: | 2-s2.0-84899687263 |
| ≡ OpenAlex: | W1973913853 |