Remarks on summability of series formed of deviation probabilities of sums of independent identically distributed random variables - Pruss, A. R. (Ukrains’kyi Matematychnyi Zhurnal, 1996)
We make some remarks leading to a refinement of the recent work of Klesov (1993) on the connection between the convergence of the series \(Σ _{n = 1}^∞ τ _n P(|S_n | \ge ε n^α )\) for every ε > 0 and the convergence of \(Σ _{n = 1}^∞ nτ _n P(|X_1 | \ge ε n^α )\) again for every ε > 0.