On the almost sure growth rate of sums of lower negatively dependent nonnegative random variables. (English) Zbl 1070.60030

Summary: For a sequence of lower negatively dependent nonnegative random variables \(\{X_n\), \(n\geq 1\}\), conditions are provided under which \(\lim_{n\to\infty} \sum_{j=1}^n X_j/b_n= \infty\) almost surely where \(\{b_n\), \(n\geq 1\}\) 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 \(b_n= n^r\), \(n\geq 1\), where \(r>0\).


60F15 Strong limit theorems
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