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

yFor a sequence of lower negatively dependent nonnegative random variables {X-n, n greater than or equal to 1}, conditions are provided under which lim(n-->infinity) Sigma(j)(=1)(n)X j/b(n) = infinity almost surely where {b(n), n greater than or equal to 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 b(n), = n(r), n greater than or equal to 1 where r > 0. (C) 2004 Elsevier B.V. All rights reserved.