Complete convergence for arrays of rowwise independent random variables (II)
Bull. Korean Math. Soc. 2000 Vol. 37, No. 2, 255-263
Soo Hak Sung
Pai Chai University
Abstract : Let $\{X_{nk},\ u_n\le k\le v_n,\ n\ge 1\}$ be an array of rowwise independent,
but not necessarily identically distributed, random variables with $EX_{nk}=0$ for all $k$ and $n.$
In this paper, we povide a domination condition under which $\sum_{k=u_n}^{v_n}X_{nk}/n^{1/p}$,
$1\le p<2,$ converges completely to zero.
Keywords : complete convergence, arrays, rowwise independent random variables, moving average
MSC numbers : 60F15
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