A Zero-One Law for the Rates of Convergence in the Birkhoff Ergodic Theorem with Continuous Time

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A Zero-One Law for the Rates of Convergence in the Birkhoff Ergodic Theorem with Continuous Time. / Kachurovskii, A. G.; Podvigin, I. V.; Svishchev, A. A.

In: Siberian Advances in Mathematics, Vol. 32, No. 3, 08.2022, p. 186-196.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{eba39b8958bb4d4eb4d7ac8ee8876c20,

title = "A Zero-One Law for the Rates of Convergence in the Birkhoff Ergodic Theorem with Continuous Time",

abstract = "We consider monotone pointwise estimates for the rates of convergence in the Birkhoffergodic theorem with continuous time. For an ergodic semiflow in a Lebesgue space, we prove thatsuch estimates hold either on a null measure set or on a full measure set. It is shown thatmonotone estimates that hold almost everywhere always exist. We study the lattice of suchestimates and also consider some questions concerning their unimprovability.",

keywords = "Birkhoff ergodic theorem, lattice of estimates, natural extension of an endomorphism, optimal estimates, rates of convergence in ergodic theorems",

author = "Kachurovskii, {A. G.} and Podvigin, {I. V.} and Svishchev, {A. A.}",

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

year = "2022",

month = aug,

doi = "10.1134/S1055134422030026",

language = "English",

volume = "32",

pages = "186--196",

journal = "Siberian Advances in Mathematics",

issn = "1055-1344",

publisher = "PLEIADES PUBLISHING INC",

number = "3",

}

RIS

TY - JOUR

T1 - A Zero-One Law for the Rates of Convergence in the Birkhoff Ergodic Theorem with Continuous Time

AU - Kachurovskii, A. G.

AU - Podvigin, I. V.

AU - Svishchev, A. A.

PY - 2022/8

Y1 - 2022/8

N2 - We consider monotone pointwise estimates for the rates of convergence in the Birkhoffergodic theorem with continuous time. For an ergodic semiflow in a Lebesgue space, we prove thatsuch estimates hold either on a null measure set or on a full measure set. It is shown thatmonotone estimates that hold almost everywhere always exist. We study the lattice of suchestimates and also consider some questions concerning their unimprovability.

AB - We consider monotone pointwise estimates for the rates of convergence in the Birkhoffergodic theorem with continuous time. For an ergodic semiflow in a Lebesgue space, we prove thatsuch estimates hold either on a null measure set or on a full measure set. It is shown thatmonotone estimates that hold almost everywhere always exist. We study the lattice of suchestimates and also consider some questions concerning their unimprovability.

KW - Birkhoff ergodic theorem

KW - lattice of estimates

KW - natural extension of an endomorphism

KW - optimal estimates

KW - rates of convergence in ergodic theorems

UR - http://www.scopus.com/inward/record.url?scp=85137813083&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/c317cece-08bc-37b8-9a66-9e30f48e615c/

U2 - 10.1134/S1055134422030026

DO - 10.1134/S1055134422030026

M3 - Article

AN - SCOPUS:85137813083

VL - 32

SP - 186

EP - 196

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 3

ER -

ID: 38058361