Сходимость рядов из вероятностей больших уклонений сумм независимых одинаково распределенных случайных величин

Abstract

The series ∑n≥1τnP(|Sn|≥ εnα) is studied, where Sn are the sums of independent equally distributed random variables, τn is a sequence of nonnegative numbers, α>0, and ε>0 is an arbitrary positive number. For a broad class of sequences τn, the necessary and sufficient conditions are established for the convergence of this series for any ε>0.