Complete convergence of the maximum partial sums for arrays of rowwise of AANA random variables (Q1956106)

Summary: The limiting behavior of the maximal partial sums \[ (1/a_n)\max_{1 \leq j \leq n}| \sum^j_{i=1} X_{ni}| \] is investigated, and some new results are obtained, where \(\{x_{ni}, i \geq 1, n \geq 1\}\) is an array of row-wise AANA random variables and \(\{a_n, n \geq 1\}\) is a sequence of positive real numbers. As an application, the Chung-type strong law of large numbers for arrays of row-wise AANA random variables is obtained. The results extend and improve the corresponding ones of \textit{T.-C. Hu} and \textit{R. L. Taylor} [Int. J. Math. Math. Sci. 20, No. 2, 375--382 (1997; Zbl 0883.60024)] for arrays of row-wise independent random variables.