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
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 is studied in this paper. More specifically, if the series 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 , 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.