ON THE RATE OF CONVERGENCE FOR THE WEAK LAW OF LARGE
NUMBERS

Robert Bartoszyński

Prem S. Puri

Abstract: Let be i.i.d. random variables with the common distribution
F. Further, let be a sequence of positive numbers, and be a strictly
increasing sequence of positive integers. The paper considers the convergence of the
series

under the interplay of three types of conditions:

(i) convergence of this series,

(ii) an appropriate moment condition on ,

(iii) a condition imposing constraints on the behavior of the sequences
and

Three theorems have been proven; in each of these two among (i)-(iii) implying the third,
with one of the theorems being valid for the general case, where the random variables
involved are not necessarily i.i.d.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -