Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variables. (English) Zbl 1294.60056

Wu, Yong-Feng; Zhu, Dong-jin

J. Korean Stat. Soc. 39, No. 2, 189-197 (2010).

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

Keywords:

negatively orthant dependent random variable; complete convergence; complete moment convergence; \(L^{1}\) convergence

Citations:

Zbl 0883.60024

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