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On the precision of approximation of the distribution function of a sum of independent random variables. (English. Russian original) Zbl 0836.60054

Theory Probab. Math. Stat. 45, 95-100 (1992); translation from Teor. Veroyatn. Mat. Stat., Kiev 45, 97-104 (1991).
Summary: Lower estimates are obtained for the quantities \(\int^\infty_{- \infty} {1 \over 1 + x^2} |\Delta (x) |dx\), \(\int^\infty_{- \infty} {1 \over 1 + x^2} |d \Delta (x) |\), where \(\Delta (x)\) is the difference between the distribution function of an almost surely convergent sum of independent random variables and the distribution function of a random variable with finite Poisson spectrum and zero mean.

MSC:

60G50 Sums of independent random variables; random walks
60E99 Distribution theory