On the almost sure growth rate of sums of lower negatively dependent nonnegative random variables

For a sequence of lower negatively dependent nonnegative random variables {Xn,n⩾1}, conditions are provided under which limn→∞∑j=1nXj/bn=∞ almost surely where {bn,n⩾1} is a nondecreasing sequence of positive constants. The results are new even when they are specialized to the case of nonnegative independent and identically distributed summands and bn=nr, n⩾1 where r>0.