Remarks on summability of series formed of deviation probabilities of sums of independent identically distributed random variables

• Date: 1996
• Main Authors: Pruss, A. R., Прус, А. Р.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 1996
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5323
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We make some remarks leading to a refinement of the recent work of Klesov (1993) on the connection between the convergence of the series \(\Sigma _{n = 1}^\infty \tau _n P(|S_n | \ge \varepsilon n^\alpha )\) for every ε > 0 and the convergence of \(\Sigma _{n = 1}^\infty n\tau _n P(|X_1...