Convergence of the series of large-deviation probabilities for sums of independent equally distributed random variables - Klesov, O. I. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
The series olimits_n 1 τ _n P(|S_n | ε n^a ) is studied, where S_n are the sums of independent equally distributed random variables, τ_n is a sequence of nonnegative numbers, α > 0, and ɛ > 0 is an arbitrary positive number. For a broad class of sequences τ_n, the necessary and sufficient conditions are established for the convergence of this series for any ɛ > 0.