Abstract
For a sequence of nonnegative random variables {Xn,n≥1} with finite means and partial sums Sn=∑i=1nXi,n≥1, and a sequence of positive numbers {bn,n≥1} with bn↑∞, sufficient conditions are given under which (Sn−ESn)/bn→0 almost surely. Our result generalizes the strong law of large numbers obtained by Korchevsky (2015). Some applications for dependent random variables are also provided.
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