2017
Том 69
№ 9

# Convergence of the series of large-deviation probabilities for sums of independent equally distributed random variables

Klesov O. I.

Abstract

The series$\sum\nolimits_{n \geqslant 1} {\tau _n P(|S_n | \geqslant \varepsilon n^a )}$ is studied, where Sn are the sums of independent equally distributed random variables, ?n is a sequence of nonnegative numbers, ?>0, and ?>0 is an arbitrary positive number. For a broad class of sequences ?n, the necessary and sufficient conditions are established for the convergence of this series for any ?>0.

English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 6, pp 845-862.

Citation Example: Klesov O. I. Convergence of the series of large-deviation probabilities for sums of independent equally distributed random variables // Ukr. Mat. Zh. - 1993. - 45, № 6. - pp. 770–784.

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