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

  • A. R. Pruss

Abstract

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 \(\Sigma _{n = 1}^\infty n\tau _n P(|X_1 | \ge \varepsilon n^\alpha )\) again for every ε > 0.
Published
25.04.1996
How to Cite
PrussA. R. “Remarks on Summability of Series Formed of Deviation Probabilities of Sums of Independent Identically Distributed Random Variables”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 48, no. 4, Apr. 1996, pp. 569-72, https://umj.imath.kiev.ua/index.php/umj/article/view/5323.
Section
Short communications