UNIVERSITY OF COLORADO COLORADO SPRINGS

COLLEGE OF ENGINEERING AND APPLIED SCIENCE

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On the Rate of Convergence of Series of Random Variables

Eunwoo Nam

US Air Force Academy

Colorado Springs, CO

The rate of convergence for an almost certainly convergent series  of random variables is studied in this presentation.  When the series  converges to a random variable  almost surely, the tail series  is a well-defined sequence of random variables with  almost surely.  We shall be concerned with the rate in which  converges to  almost surely (or in probability), or equivalently, in which the tail series  converges to 0 almost surely (or in probability). More specifically, tail series strong laws of large number and tail series weak laws of large numbers will be introduced, and their relationship will also be investigated.