On the limiting behavior of the maximum partial sums for arrays of rowwise NA random variables. (English) Zbl 1125.60027

Gan, Shixin; Chen, Pingyan

Acta Math. Sci., Ser. B, Engl. Ed. 27, No. 2, 283-290 (2007).

Summary: Let \( \{X_{ni}\), \(i \leq n\), \(i < \infty \}\) be an array of rowwise NA random variables and \(\{a_n, n \geq 1\}\) a sequence of constants with \( 0 < a_n \uparrow \infty\) . The limiting behavior of maximum partial sums \({\frac1{a_n}} \max_{1 \leqslant k \leqslant n} | \sum^k_{i=1}X_{ni}|\) is 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)] and T.-C. Hu and H.-C. Chang [Soochow J. Math. 20, No. 4, 587–594 (1994; Zbl 0861.60014)].

MSC:

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

Keywords:

NA random variable; maximum partial sum; complete convergence; convergent in probability

Citations:

Zbl 0883.60024; Zbl 0861.60014