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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 11, Pages 789-794
doi:10.1155/S0161171200003112

Complete convergence for sums of arrays of random elements

Soo Hak Sung

Department of Applied Mathematics, Pai Chai University, Taejon 302-735, South Korea

Abstract

Let {Xni} be an array of rowwise independent B-valued random elements and {an} constants such that 0<an↑∞. Under some moment conditions for the array, it is shown that ∑i=1nXni/an converges to 0 completely if and only if ∑i=1nXni/an converges to 0 in probability.