Interrelation between the convergence rates in von Neumann’s and Birkhoff’s ergodic theorems | Sciact - Система учета научной деятельности ИМ СО РАН

Interrelation between the convergence rates in von Neumann’s and Birkhoff’s ergodic theorems Научная публикация

Журнал

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

Вых. Данные

Год: 2014, Том: 55, Номер: 2, Страницы: 336-348 Страниц : 13 DOI: 10.1134/s0037446614020165

Ключевые слова

von Neumann’s ergodic theorem, Birkhoff’s ergodic theorem, convergence rate of ergodic averages, wide-sense stationary stochastic process, contraction semigroups in Lp

Авторы

Sedalishchev V.V. ¹

Организации

1	Novosibirsk state university

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.

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

Поступила в редакцию:	14 июн. 2013 г.
Опубликована в печати:	30 апр. 2014 г.
Опубликована online:	30 апр. 2014 г.

≡ Web of science:	WOS:000335167300016
≡ Scopus:	2-s2.0-84899687263
≡ OpenAlex:	W1973913853