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Mat. Zametki, 1998, Volume 64, Issue 3, Pages 366–372 (Mi mz1406)  

This article is cited in 12 scientific papers (total in 12 papers)

Decrease rate of the probabilities of $\varepsilon$-deviations for the means of stationary processes

V. F. Gaposhkin

Moscow State University of Railway Communications

Abstract: The asymptotic behavior as $n\to\infty$ of the normed sums $\sigma_n=n^{-1}\sum_{k=0}^{n-1}X_k$ for a stationary process $X=(X_n, n\in\mathbb Z)$ is studied. For a fixed $\varepsilon>0$, upper estimates for $\mathsf P(\sup_{k\ge n} |\sigma_k|\ge\varepsilon)$ as $n\to\infty$ are obtained.

DOI: https://doi.org/10.4213/mzm1406

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English version:
Mathematical Notes, 1998, 64:3, 316–321

Bibliographic databases:

UDC: 519
Received: 01.09.1997

Citation: V. F. Gaposhkin, “Decrease rate of the probabilities of $\varepsilon$-deviations for the means of stationary processes”, Mat. Zametki, 64:3 (1998), 366–372; Math. Notes, 64:3 (1998), 316–321

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Gaposhkin, VF, “Some examples of the problem of epsilon-deviations for stationary sequences”, Theory of Probability and Its Applications, 46:2 (2001), 341  crossref  mathscinet  zmath  isi  scopus  scopus
    2. V. F. Gaposhkin, “Estimates of the Entropy of the Set of Means for Some Classes of Stationary and Quasistationary Sequences”, Math. Notes, 78:1 (2005), 47–52  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. V. F. Gaposhkin, “Exact Estimates of the Metric Entropy of the Averages for Some Classes of Stationary Sequences”, Theory Probab. Appl., 53:1 (2009), 37–58  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. A. G. Kachurovskii, A. V. Reshetenko, “On the rate of convergence in von Neumann's ergodic theorem with continuous time”, Sb. Math., 201:4 (2010), 493–500  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. A. G. Kachurovskii, V. V. Sedalishchev, “Constants in estimates for the rates of convergence in von Neumann's and Birkhoff's ergodic theorems”, Sb. Math., 202:8 (2011), 1105–1125  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Kachurovskii A.G., Sedalischev V.V., “Neravenstva, pozvolyayuschie otsenivat skorosti skhodimosti v ergodicheskikh teoremakh”, Vestnik Kemerovskogo gosudarstvennogo universiteta, 2011, no. 3-1, 250–254  elib
    7. A. G. Kachurovskii, V. V. Sedalishchev, “On the Constants in the Estimates of the Rate of Convergence in the Birkhoff Ergodic Theorem”, Math. Notes, 91:4 (2012), 582–587  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    8. V. V. Sedalishchev, “Constants in the estimates of the convergence rate in the Birkhoff ergodic theorem with continuous time”, Siberian Math. J., 53:5 (2012), 882–888  mathnet  crossref  mathscinet  isi
    9. Gomilko A., Haase M., Tomilov Yu., “Bernstein Functions and Rates in Mean Ergodic Theorems for Operator Semigroups”, J. Anal. Math., 118 (2012), 545–576  crossref  mathscinet  zmath  isi  scopus  scopus
    10. V. V. Sedalishchev, “Interrelation between the convergence rates in von Neumann's and Birkhoff's ergodic theorems”, Siberian Math. J., 55:2 (2014), 336–348  mathnet  crossref  mathscinet  isi
    11. A. G. Kachurovskii, I. V. Podvigin, “Estimates of the rate of convergence in the von Neumann and Birkhoff ergodic theorems”, Trans. Moscow Math. Soc., 77 (2016), 1–53  mathnet  crossref  elib
    12. Kachurovskii A.G., Podvigin I.V., “Fejer Sums For Periodic Measures and the Von Neumann Ergodic Theorem”, Dokl. Math., 98:1 (2018), 344–347  crossref  mathscinet  zmath  isi  scopus
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