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On stability of sums of nonnegative random variables. (English. Russian original) Zbl 1180.60031

J. Math. Sci., New York 159, No. 3, 324-326 (2009); translation from Zap. Nauchn. Semin. POMI 361, 78-82 (2008).
Summary: 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.

MSC:

60F15 Strong limit theorems
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References:

[1] B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison–Wesley, Reading (1968). · Zbl 0056.36001
[2] N. Etemadi, ”Stability of sums of weighted nonnegative random variables,” J. Multivar. Anal., 13, 361–365 (1983). · Zbl 0531.60034
[3] V. V. Petrov, Sums of Independent Random Variables, Springer, New York (1975). · Zbl 0322.60043
[4] V. V. Petrov, ”On the strong law of large numbers for sequences of nonnegative random variables,” Teor. Veroyatn. Primen., 53, 379–382 (2008).
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