On Convergence Rates in the Birkhoff Ergodic Theorem

被引：0
作者：
Podvigin, I. V. [1 ]
机构：
[1] Sobolev Inst Math, Novosibirsk, Russia
来源：
SIBERIAN MATHEMATICAL JOURNAL | 2024年 / 65卷 / 05期
关键词：
convergence rates in ergodic theorems; correlations; large deviations; 517.987; LARGE DEVIATIONS; STATISTICAL PROPERTIES; MARKOV APPROXIMATIONS; POINTWISE CONVERGENCE; DYNAMICAL-SYSTEMS; RECURRENCE TIMES; LIMIT-THEOREMS; LARGE NUMBERS; AVERAGES; DECAY;
D O I：
10.1134/S0037446624050161
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Basing on two approaches, we survey the results about convergence rates in the Birkhoff Ergodic Theorem. The first approach concerns almost everywhere pointwise estimates of ergodic averages, whereas the second relies upon the estimates of the measures of maximal deviations.
引用
收藏
页码：1170 / 1186
页数：17
相关论文
共 105 条
  • [1] Joint coboundaries
    Adams, Terry
    Rosenblatt, Joseph
    [J]. DYNAMICAL SYSTEMS, ERGODIC THEORY, AND PROBABILITY: IN MEMORY OF KOLYA CHERNOV, 2017, 698 : 5 - 33
  • [2] Large deviations for dynamical systems with stretched exponential decay of correlations
    Aimino, Romain
    Freitas, Jorge Milhazes
    [J]. PORTUGALIAE MATHEMATICA, 2019, 76 (02) : 143 - 152
  • [3] From rates of mixing to recurrence times via large deviations
    Alves, Jose F.
    Freitas, Jorge M.
    Luzzatto, Stefano
    Vaienti, Sandro
    [J]. ADVANCES IN MATHEMATICS, 2011, 228 (02) : 1203 - 1236
  • [4] [Anonymous], 2006, Handbook of Dynamical Systems, V1B, P244
  • [5] Antonevich AB, 2022, SB MATH+, V213, P891, DOI 10.4213/sm9356e
  • [6] Deviation of ergodic averages for rational polygonal billiards
    Athreya, J. S.
    Forni, G.
    [J]. DUKE MATHEMATICAL JOURNAL, 2008, 144 (02) : 285 - 319
  • [7] RECURRENCE OF CO-CYCLES AND RANDOM-WALKS
    ATKINSON, G
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1976, 13 (AUG): : 486 - 488
  • [8] Baladi V., 2000, Positive Operators and Decay of Correlations, DOI [10.1142/3657, DOI 10.1142/3657]
  • [9] Bari NK, 1956, PROC MOSC MATH SOC, V5, P483
  • [10] Fast and slow points of Birkhoff sums
    Bayart, Frederic
    Buczolich, Zoltan
    Heurteaux, Yanick
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2020, 40 (12) : 3236 - 3256
12345678910