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Teoriya Veroyatnostei i ee Primeneniya, 1975, Volume 20, Issue 1, Pages 134–140 (Mi tvp2996)  

This article is cited in 109 scientific papers (total in 110 papers)

Short Communications

A note on the central limit theorems for dependent random variables

I. A. Ibragimov

Leningrad
Abstract: The paper contains a few limit theorems for stationary sequences {ξj} under the condition ρ(n)0, where ρ(n) denotes the maximal correlation coefficient between the past {ξj,j0} and the future {ξj,jn} of the sequence {ξj}.
Received: 05.05.1974
English version:
Theory of Probability and its Applications, 1975, Volume 20, Issue 1, Pages 135–141
DOI: https://doi.org/10.1137/1120011
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. A. Ibragimov, “A note on the central limit theorems for dependent random variables”, Teor. Veroyatnost. i Primenen., 20:1 (1975), 134–140; Theory Probab. Appl., 20:1 (1975), 135–141
Citation in format AMSBIB
\Bibitem{Ibr75}
\by I.~A.~Ibragimov
\paper A~note on the central limit theorems for dependent random variables
\jour Teor. Veroyatnost. i Primenen.
\yr 1975
\vol 20
\issue 1
\pages 134--140
\mathnet{http://mi.mathnet.ru/tvp2996}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=362448}
\zmath{https://zbmath.org/?q=an:0335.60023}
\transl
\jour Theory Probab. Appl.
\yr 1975
\vol 20
\issue 1
\pages 135--141
\crossref{https://doi.org/10.1137/1120011}
Linking options:
  • https://www.mathnet.ru/eng/tvp2996
  • https://www.mathnet.ru/eng/tvp/v20/i1/p134
  • This publication is cited in the following 110 articles:
    1. Daniel Odens Mora, Alberto Aliseda, Alain Cartellier, Martin Obligado, “Characterizing inertial particle clustering with 1D signals”, Meas. Sci. Technol., 35:2 (2024), 025302  crossref
    2. Magda Peligrad, “On the Quenched CLT for Stationary Markov Chains”, J Theor Probab, 37:1 (2024), 603  crossref
    3. Martial Longla, “On some extremes of mixing for Copula-based Markov chains”, Contributions to Pure and Applied Mathematics, 2:1 (2024)  crossref
    4. A. A. Borovkov, Al. V. Bulinski, A. M. Vershik, D. Zaporozhets, A. S. Holevo, A. N. Shiryaev, “Ildar Abdullovich Ibragimov (on his ninetieth birthday)”, Russian Math. Surveys, 78:3 (2023), 573–583  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    5. A. A. Kudryavtsev, O. V. Shestakov, “Metod otsenivaniya parametrov raspredeleniya po vyborke so slabo zavisimymi komponentami”, Inform. i ee primen., 17:3 (2023), 58–63  mathnet  crossref
    6. José Alfredo Sánchez de León, “Determination of eddy currents equipment parameters: [cutting_tolerance], [cutting_position]”, Journal of Computational and Applied Mathematics, 425 (2023), 115023  crossref
    7. Florence Merlevède, Magda Peligrad, Progress in Probability, 80, High Dimensional Probability IX, 2023, 229  crossref
    8. Olimjon Sh. Sharipov, Anvar F. Norjigitov, “Central limit theorem for weakly dependent random variables with values in $D\left[0,1\right]$”, Zhurn. SFU. Ser. Matem. i fiz., 15:3 (2022), 281–291  mathnet  crossref  mathscinet
    9. D. O. Mora, M. Bourgoin, P. D. Mininni, M. Obligado, “Clustering of vector nulls in homogeneous isotropic turbulence”, Phys. Rev. Fluids, 6:2 (2021)  crossref
    10. Ilya Dumer, Navid Gharavi, 2021 IEEE International Symposium on Information Theory (ISIT), 2021, 238  crossref
    11. Richard C. Bradley, Richard A. Davis, Dimitris N. Politis, “Preface to the Murray Rosenblatt memorial special issue of JTSA”, Journal Time Series Analysis, 42:5-6 (2021), 495  crossref
    12. Diandian Ma, Xiaojing Song, Mark Tippett, Thu Phuong Truong, “Accumulated (integrated) interest and the square root process”, ARJ, 32:4 (2019), 678  crossref
    13. Abdelaati Daouia, Stéphane Girard, Gilles Stupfler, “Extreme M-quantiles as risk measures: From $L^{1}$ to $L^{p}$ optimization”, Bernoulli, 25:1 (2019)  crossref
    14. Erwan Koch, Clément Dombry, Christian Y. Robert, “A central limit theorem for functions of stationary max-stable random fields on Rd”, Stochastic Processes and their Applications, 129:9 (2019), 3406  crossref
    15. Lorenzo Finesso, Peter Spreij, “Approximation of nonnegative systems by moving averages of fixed order”, Automatica, 107 (2019), 1  crossref
    16. Dennis DeRiggi, “A central limit theorem for correlated variables with limited normal or gamma distributions”, Communications in Statistics - Theory and Methods, 48:21 (2019), 5213  crossref
    17. Ibragimov I.A. Lifshits M.A. Nazarov A.I. Zaporozhets D.N., “On the History of St. Petersburg School of Probability and Mathematical Statistics: II. Random Processes and Dependent Variables”, Vestn. St Petersb. Univ.-Math., 51:3 (2018), 213–236  crossref  isi  scopus
    18. Youngjun Choe, Henry Lam, Eunshin Byon, “Uncertainty Quantification of Stochastic Simulation for Black-box Computer Experiments”, Methodol Comput Appl Probab, 20:4 (2018), 1155  crossref
    19. Xin Guo, Adrien de Larrard, Zhao Ruan, “Optimal placement in a limit order book: an analytical approach”, Math Finan Econ, 11:2 (2017), 189  crossref
    20. Béatrice Bucchia, Martin Wendler, “Change-point detection and bootstrap for Hilbert space valued random fields”, Journal of Multivariate Analysis, 155 (2017), 344  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
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