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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 $$\{X_n$$, $$n\geq 1\}$$, 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 $$r>0$$.

##### MSC:
 60F15 Strong limit theorems
Full Text:
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