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The concentration functions of sums of independent random variables

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Proceedings of the Second Japan-USSR Symposium on Probability Theory

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References

  1. K.L. Chung and P. Erdös: Probability limit theorems assuming only the first moment, Mem.Amer.Math.Soc., (1951).

    Google Scholar 

  2. W. Doeblin et P. Lévy: Sur les sommes de variables aléatoires à dispersions bornés inferieurement, C.R.Acad.Sci. Paris, 902 (1936), 2027–2029.

    MATH  Google Scholar 

  3. W. Doeblin: Sur les sommes d'un grand nombre des variables aléatoires independantes, Bull.Sci.Math., 63(1939), 23–64.

    MATH  Google Scholar 

  4. J.E.A. Dunnage: Inequalities for concentration of sums of independent random variables, Proc.London Math.Soc., (3) 23(1971), 489–514.

    Article  MathSciNet  MATH  Google Scholar 

  5. P. Erdös: On a lemma of Littlewood and Offord, Bull.Amer.Math.Soc., 51(1945), 898–902

    Article  MathSciNet  MATH  Google Scholar 

  6. C.-G. Esseen: On the Kolmogorov-Rogozin inequality for the concentration function, Z. Wahrscheinlichkeitstheorie verw.Geb., 5(1966), 210–216.

    Article  MathSciNet  MATH  Google Scholar 

  7. C.-G. Esseen: On the concentration function of a sum of independent random variables, Z. Wahrscheinlichkeitstheorie verw. Geb., 9(1968), 290–308.

    Article  MathSciNet  MATH  Google Scholar 

  8. H. Kesten: A sharper form of the Doeblin-Levy-Kolmogorov-Rogozin inequality for concentration functions, Math.Scand., 25(1969), 133–144.

    MathSciNet  MATH  Google Scholar 

  9. A. Kolmogorov: Two uniform limit theorems for sums of independent random variables, Theor.Prob.Appl., 1(1956), 384–394.

    Article  Google Scholar 

  10. A. Kolmogorov: Sur les proprietes des fonctions de concentrations de M.P.Lévy, Ann.Inst.Henri Poincaré, 16(1958), 27–34.

    MathSciNet  MATH  Google Scholar 

  11. A. Kolmogorov: On the approximation of distributions of sums of independent summands by infinitely divisible distributions, Sankhya, Ser A 25 (1963), 159–174.

    MathSciNet  MATH  Google Scholar 

  12. L. LeCam: On the distribution of sums of independent random variables, Bernoulli, Bayes, Laplace, ed. by J. Neyman and L. LeCam, Berlin-Heidelberg-New York: Springer, 1965, 179–220.

    Google Scholar 

  13. P. Lévy: Theorie de l'addition des variables aleatoires, 2 ed., Gauthier-Villars, Paris 1954.

    MATH  Google Scholar 

  14. J.E. Littlewood and A.C. Offord: On the number of real roots of a random algebraic equation, III, Recueil Math., 5, 12(1943), 277–286.

    MathSciNet  MATH  Google Scholar 

  15. Д. Д. Мещалкин, Обобщение теоремы Щпернера о числе додмножеств конечного множества, Теория вероят.и ее примен., 8(1963),219–220.

    Google Scholar 

  16. A.C. Offord: An inequality for sums of independent random variables, Proc.London Math.Soc., (2) 48 (1945), 467–477.

    Article  MathSciNet  MATH  Google Scholar 

  17. В.И. Паулаускас, О функЦиях концентрации случайних векторов, ДАН СССР, 204(1972), 791–794.

    Google Scholar 

  18. В.В. Петров, Об оценке функций концентраций суммн неэависимых случайных величихn, Теория вероят. и ее примен., 15(1970), 718–721.

    Google Scholar 

  19. Ю.В.Прохоров, Экстремальхые эадачи в предельных теоремах, Труды б Всесоюэного совещания по теории вероятностей и математической статистике, Вильнюс, 1962, 77–84.

    Google Scholar 

  20. B.A. Rogozin: An estimate for concentration functions, Theor. Probab.Appl., 6(1961), 94–97.

    Article  MathSciNet  MATH  Google Scholar 

  21. B.A. Rogozin: On the increase of dispersion of sums of independent random variables, Theor.Probab.Appl., 6(1961), 97–99.

    Article  MathSciNet  MATH  Google Scholar 

  22. B. Rosén: On the asymptotic distribution of sums of independent random variables, Ark.Mat., 4(1961), 323–332.

    Article  MathSciNet  MATH  Google Scholar 

  23. В.В. Саэонов, О многомерных Функциях концентрации, Теория вероят. и ее примех., II (1966), 683–690.

    Google Scholar 

  24. Б.А. Севастбянов, О многомерных Функциях концентрации, Теория вероят. и ее примен., 8 (1963), 124–125.

    Google Scholar 

  25. E. Sperner: Ein Satz über Untermengen einer endlichen Menge, Math.Z., 27(1928), 544–548.

    Article  MathSciNet  MATH  Google Scholar 

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G. Maruyama Yu. V. Prokhorov

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© 1973 Springer-Verlag

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Rogozin, B.A. (1973). The concentration functions of sums of independent random variables. In: Maruyama, G., Prokhorov, Y.V. (eds) Proceedings of the Second Japan-USSR Symposium on Probability Theory. Lecture Notes in Mathematics, vol 330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061502

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  • DOI: https://doi.org/10.1007/BFb0061502

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  • Print ISBN: 978-3-540-06358-2

  • Online ISBN: 978-3-540-46956-8

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