On Possible Estimates of the Rate of Pointwise Convergence in the Birkhoff Ergodic Theorem

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On Possible Estimates of the Rate of Pointwise Convergence in the Birkhoff Ergodic Theorem. / Podvigin, I. V.

в: Siberian Mathematical Journal, Том 63, № 2, 03.2022, стр. 316-325.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{54455a74cc8d43ae9b463a09ef1398fc,

title = "On Possible Estimates of the Rate of Pointwise Convergence in the Birkhoff Ergodic Theorem",

abstract = "We study the separation from zero of a sequence ϕϕ to obtain the estimates of the form ϕ(n)/nϕ(n)/n for the rate of pointwise convergence of ergodic averages. Each of these ϕϕ is shown to be separated from zero for mixings which is not always so for weak mixings. Moreover, for the characteristic function of a nontrivial set, it is shown that there exists a measure preserving transformation with arbitrarily slow decay of ergodic averages.",

keywords = "517.987, Birkhoff ergodic theorem, ergodic theorems for subsequences, rate of convergence in ergodic theorems",

author = "Podvigin, {I. V.}",

note = "Publisher Copyright: {\textcopyright} 2022, Pleiades Publishing, Ltd.",

year = "2022",

month = mar,

doi = "10.1134/S0037446622020094",

language = "English",

volume = "63",

pages = "316--325",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",

number = "2",

}

RIS

TY - JOUR

T1 - On Possible Estimates of the Rate of Pointwise Convergence in the Birkhoff Ergodic Theorem

AU - Podvigin, I. V.

PY - 2022/3

Y1 - 2022/3

N2 - We study the separation from zero of a sequence ϕϕ to obtain the estimates of the form ϕ(n)/nϕ(n)/n for the rate of pointwise convergence of ergodic averages. Each of these ϕϕ is shown to be separated from zero for mixings which is not always so for weak mixings. Moreover, for the characteristic function of a nontrivial set, it is shown that there exists a measure preserving transformation with arbitrarily slow decay of ergodic averages.

AB - We study the separation from zero of a sequence ϕϕ to obtain the estimates of the form ϕ(n)/nϕ(n)/n for the rate of pointwise convergence of ergodic averages. Each of these ϕϕ is shown to be separated from zero for mixings which is not always so for weak mixings. Moreover, for the characteristic function of a nontrivial set, it is shown that there exists a measure preserving transformation with arbitrarily slow decay of ergodic averages.

KW - 517.987

KW - Birkhoff ergodic theorem

KW - ergodic theorems for subsequences

KW - rate of convergence in ergodic theorems

UR - http://www.scopus.com/inward/record.url?scp=85127770835&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/17423eef-a941-3abd-92ab-28040384890d/

U2 - 10.1134/S0037446622020094

DO - 10.1134/S0037446622020094

M3 - Article

AN - SCOPUS:85127770835

VL - 63

SP - 316

EP - 325

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 2

ER -

ID: 35879587