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• W2077554328 abstract "Previous article Next article On the Convergence Rate in the Central Limit Theorem for Weakly Dependent Random VariablesA. N. TikhomirovA. N. Tikhomirovhttps://doi.org/10.1137/1125092PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Yu. A. Davydov, Convergence of distributions generated by stationary stochastic processes, Theory Prob. Appl., 13 (1968), 691–696 LinkGoogle Scholar[2] Yu. A. Davydov, Mixing conditions for Markov chains, Theory Prob. Appl., 18 (1973), 312–328 LinkGoogle Scholar[3] I. A. Ibragimov and , Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971, 443– 48:1287 0219.60027 Google Scholar[4] A. V. Nagaev, Limit theorems that take into account large deviations when Cramér's condition is violated, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, 13 (1969), 17–22, (In Russian.) 43:8108 0226.60043 Google Scholar[5] V. V. Petrov, Sums of independent random variables, Springer-Verlag, New York, 1975x+346 52:9335 CrossrefGoogle Scholar[6] V. A. Statulyavichus, On limit theorems for dependent random variables, Second Vilnius Conf. on Prob. Theory and Math. Statistics, Abstracts of Reports, Vol. 3, Vilnius, 1977, 212–215, (In Russian.) Google Scholar[7] A. N. Tikhomirov, The rate of convergence in the central limit theorem for weakly dependent variables, Vestnik Leningrad. Univ., (1976), 158–159, 166, (In Russian.) 56:9651 0346.60016 Google Scholar[8] A. N. Tikhomirov, The convergence rate in the central limit theorem for Markov chains, Theory Prob. Appl., 20 (1975), 676–677 Google Scholar[9] Kai Lai Chung, Markov chains with stationary transition probabilities, Second edition. Die Grundlehren der mathematischen Wissenschaften, Band 104, Springer-Verlag New York, Inc., New York, 1967xi+301, 2nd ed. 36:961 0146.38401 Google Scholar[10] Charles Stein, A bound for the error in the normal approximation to the distribution of a sum of dependent random variables, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability theory, Univ. California Press, Berkeley, Calif., 1972, 583–602 53:6687 0278.60026 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails KOLMOGOROV BOUNDS FOR THE NORMAL APPROXIMATION OF THE NUMBER OF TRIANGLES IN THE ERDŐS–RÉNYI RANDOM GRAPH8 March 2021 | Probability in the Engineering and Informational Sciences, Vol. 36, No. 3 Cross Ref A semiparametric latent factor model for large scale temporal data with heteroscedasticityJournal of Multivariate Analysis, Vol. 186 Cross Ref Simulating risk measures via asymptotic expansions for relative errors30 March 2021 | Mathematical Finance, Vol. 31, No. 3 Cross Ref Assessment of Impact of AC Circuit Attributes to Outage Frequency in the WECC SystemIEEE Transactions on Power Delivery, Vol. 36, No. 2 Cross Ref On the rate of convergence to normality of estimates of regression coefficient for associated random fields22 December 2020 | Prykladni Problemy Mekhaniky i Matematyky, Vol. 18, No. 0 Cross Ref Optimum Performance of Short Block Length Codes Under Multivariate Stationary Rayleigh FadingIEEE Transactions on Wireless Communications, Vol. 19, No. 3 Cross Ref Entropy, Vol. 22, No. 4 Cross Ref Convergence of sums of dependent Bernoulli random variables: an application from portfolio theory4 December 2018 | Communications in Statistics - Theory and Methods, Vol. 48, No. 23 Cross Ref Second Order Analysis for Joint Source-Channel Coding With General Channel and Markovian SourceIEEE Transactions on Information Theory, Vol. 65, No. 9 Cross Ref The Berry--Esseen Bound for $rho$-Mixing Random Variables and Its Applications in Nonparametric Regression ModelX. 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Abdalimov17 July 2006 | Theory of Probability & Its Applications, Vol. 27, No. 2AbstractPDF (505 KB) Volume 25, Issue 4| 1981Theory of Probability & Its Applications History Submitted:18 January 1979Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1125092Article page range:pp. 790-809ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics" @default.
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