Journal of Applied Mathematics and Stochastic Analysis
Volume 2004 (2004), Issue 2, Pages 159-168

On the order of growth of convergent series of independent random variables

Eunwoo Nam

Department of Mathematical Sciences, United States Air Force Academy (USAFA), CO 80840, USA

Received 8 May 2003; Revised 30 January 2004

Copyright © 2004 Eunwoo Nam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.