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

• Date: 1993
• Main Authors: Klesov, O. I., Клесов, О. И.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1993
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5866
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

The series $\sum\nolimits_{n \geqslant 1} {\tau _n P(|S_n | \geqslant \varepsilon n^a )}$ 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...