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An elementary derivation of Khintchine's estimate for large deviations.


Author: Mark Pinsky
Journal: Proc. Amer. Math. Soc. 22 (1969), 288-290
MSC: Primary 60.30
DOI: https://doi.org/10.1090/S0002-9939-1969-0245078-6
MathSciNet review: 0245078
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References [Enhancements On Off] (What's this?)

  • [1] Kai Lai Chung, A course in probability theory, Harcourt, Brace & World, Inc., New York, 1968. MR 0229268
  • [2] A. Y. Khintchine, Asymptotische Gesetze der Wahrscheinlichkeitrechung, Ergebnisse der Math., Vol. 2, Springer-Berlin, Berlin, 1933.
  • [3] John Lamperti, Probability. A survey of the mathematical theory, W. A. Benjamin, Inc., New York-Amsterdam, 1966. MR 0206996
  • [4] V. V. Petrov, On a relation between an estimate of the remainder in the central limit theorem and the law of iterated logarithm, Teor. Verojatnost. i Primenen 11 (1966), 514–518 (Russian, with English summary). MR 0212855
  • [5] H. F. Trotter, An elementary proof of the central limit theorem, Arch. Math. 10 (1959), 226–234. MR 0108847, https://doi.org/10.1007/BF01240790

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DOI: https://doi.org/10.1090/S0002-9939-1969-0245078-6
Article copyright: © Copyright 1969 American Mathematical Society