Journal of Mathematical Sciences

, Volume 199, Issue 2, pp 162–167 | Cite as

On Approximation of Convolutions by Accompanying Laws in the Scheme of Series

  • A. Yu. Zaitsev

The problem of approximation of convolutions by accompanying laws in the scheme of series satisfying the infinitesimality condition is considered. It is shown that the quality of approximation depends essentially on the choice of centering constants.


Convolution Independent Random Variable Triangular Array Divisible Distribution Distribution Versus 
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  1. 1.
    T. V. Arak and A. Y. Zaitsev, Uniform Limit Theorems for Sums of Independent Random Variables, Trudy Mat. Inst. AN SSSR, 174 (1986)Google Scholar
  2. 2.
    Y. Davydov and V. Rotar’, “On Asymptotic proximity of distributions,” J. Theoret. Probab., 22, 82–98 (2009).CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables [in Russian] Moscow (1949).Google Scholar
  4. 4.
    I. A. Ibragimov and E. L. Presman, “The rate of convergence of distributions of sums of independent random variables with accompanying laws,” Teor. Veroyatn. Primen., 18, 753–766 (1973).MathSciNetGoogle Scholar
  5. 5.
    A. N. Kolmogorov, “Some works of recent years in the field of probability theory,” Vestn. Mosk. Univ., 7, 29–38 (1953).Google Scholar
  6. 6.
    A. N. Kolmogorov, “Two uniform limit theorems for sums of independent variables,” Teor. Veroyatn. Primen., 1, 426–436 (1956).MathSciNetGoogle Scholar
  7. 7.
    V. V. Petrov, Sums of Independent Random Variables [in Russian], Moscow (1972).Google Scholar
  8. 8.
    Yu. V. Prokhorov, “Asymptotic behavior of the binomial distribution,” Usp. Mat. Nauk, 8, 135–142 (1953).Google Scholar
  9. 9.
    A. Yu. Zaitsev and T. V. Arak, “An estimate for the rate of convergence in the second uniform limit theorem of Kolmogorov,” Teor. Veroyatn. Primen., 28, 333–353 (1983).MATHMathSciNetGoogle Scholar
  10. 10.
    A. Yu. Zaitsev, “A multidimensional variant of Kolmogorov’s second uniform limit theorem.” Teor. Verpyatn. Primen., 34, 128–151 (1989).Google Scholar
  11. 11.
    A. Yu. Zaitsev, “Estimates for the strong approximation in multidimensional central limit theorem,” in: Proc. Intern. Congr. Math., Vol. III. Invited lectures (Beijing, 2002), Higher Ed. Press, Beijing (2002), pp. 107-116.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia

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