On stability of sums of nonnegative random variables

  • V. V. Petrov

We present new sufficient conditions for stability of sums of nonnegative random variables having finite moments of second order. We demonstrate that these conditions are nonimprovable in some sense. Bibliography: 4 titles.


Russia Nonnegative Random Variable Finite Moment 
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    B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison–Wesley, Reading (1968).Google Scholar
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    N. Etemadi, “Stability of sums of weighted nonnegative random variables,” J. Multivar. Anal., 13, 361–365 (1983).MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    V. V. Petrov, Sums of Independent Random Variables, Springer, New York (1975).Google Scholar
  4. 4.
    V. V. Petrov, “On the strong law of large numbers for sequences of nonnegative random variables,” Teor. Veroyatn. Primen., 53, 379—382 (2008).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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