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Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variables. (English) Zbl 1294.60056
Summary: Let \(\{X_{nk}, 1\leq k\leq n, n\geq 1\}\) be an array of rowwise negatively orthant dependent random variables and let \(\{a_{n}, n\geq 1\}\) be a sequence of positive real numbers with \(a_{n}\uparrow\infty\). The convergence properties of partial sums \(\frac{1}{a_n} \sum^n_{k=1} X_{nk}\) are investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by T.-C. Hu and R. L. Taylor [Int. J. Math. Math. Sci. 20, No. 2, 375–382 (1997; Zbl 0883.60024)].

MSC:
60F15 Strong limit theorems
60G50 Sums of independent random variables; random walks
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