## On the strong rates of convergence for arrays of rowwise negatively dependent random variables.(English)Zbl 1223.60023

The now classical Hsu-Robbins-Erdős-Spitzer-Baum-Katz theorem concerns moment conditions for the convergence of $\sum^\infty_{n=1} n^{(r/p)- 2} P(|S_n|>\varepsilon n^{1/p}),$ where $$r> 0$$, $$0< p< 2$$, $$r\geq p$$ and where $$S_n$$ is a sum of $$n$$ i.i.d. random variables. This result has been extended in various directions over the last couple of decades.
In the present paper $$S_n$$ is replaced by $$S_{k_n}$$ which, for every $$n$$, is a sum of the $$k$$, negatively dependent random variables of the $$n$$th row of an array, and the weights are more general than powers.

### MSC:

 60F15 Strong limit theorems
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### References:

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