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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 $\{X_n$, $n\ge 1\}$, conditions are provided under which $\lim_{n\to\infty} \sum_{j=1}^n X_j/b_n= \infty$ almost surely where $\{b_n$, $n\ge 1\}$ 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 $b_n= n^r$, $n\ge 1$, where $r>0$.

60F15Strong limit theorems
Full Text: DOI
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