Abstract
The paper is devoted to the derivation of the "possibly sharpest" estimates at the investigation of the deviation of the distribution function of the normalized sum of independent random variables from the distribution function of the normal law.
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References
I. A. Ibragimov and Yu. V. Linnik, Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff, Groningen, 1971.
V. V. Petrov, Limit Theorems for Sums of Independent Random Variables [in Russian], Nauka, Moscow (1987).
V. V. Petrov, Sums of Independent Random Variables, Springer, New York (1975).
A. N. Kolmogorov, "Some works of recent years in the field of limit theorems in the theory of probability," Vestnik Moskov. Univ. Ser. Fiz.-Mat. Estest. Nauk, No. 10, 29–38 (1953).
Yu. V. Linnik, "On the accuracy of the approximation to the Gauss distribution by sums of independent random variables," Izv. Akad. Nauk SSSR, Ser. Mat.,11, No. 2, 111–138 (1947).
V. V. Petrov, "On sharp estimates in limit theorems," Dokl. Akad. Nauk SSSR,104, No. 2, 180–182 (1955).
A. Ya. Khinchin, Continued Fractions, The University of Chicago Press, Chicago (1964).
C. G. Esseen, "A moment inequality with an application to the central limit theorem," Skand. Aktuarietidskr.,39, 160–170 (1956).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 289–319, 1990.
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Chistyakov, G.P. On a problem of A. N. Kolmogorov. J Math Sci 68, 604–625 (1994). https://doi.org/10.1007/BF01254289
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DOI: https://doi.org/10.1007/BF01254289