Journal of Applied Mathematics and Stochastic Analysis
Volume 2004 (2004), Issue 2, Pages 159-168
doi:10.1155/S1048953304305022
Abstract
For independent random variables, the order of growth of the convergent series Sn is studied in this paper. More specifically, if the series Sn converges almost surely to a random variable, the tail series is a well-defined sequence of random variables and converges to 0 almost surely. For the almost surely convergent series Sn, a tail series strong law of large numbers (SLLN) is constructed by investigating the duality between the limiting behavior of partial sums and that of tail series.