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COMPLETE CONVERGENCE FOR ARRAYS OF ROWWISE INDEPENDENT RANDOM VARIABLES
Hu, Tien-Chung,Sung, Soo-Hak,Volodin, Andrei Korean Mathematical Society 2003 대한수학회논문집 Vol.18 No.2
Under some conditions on an array of rowwise independent random variables, Hu et at. (1998) obtained a complete convergence result for law of large numbers with rate {a$\_$n/, n $\geq$ 1} which is bounded away from zero. We investigate the general situation for rate {a$\_$n/, n $\geq$ 1) under similar conditions.
성수학,Tien-Chung Hu,Andrei I. Volodin 대한수학회 2006 대한수학회보 Vol.43 No.3
Sung et al. [13] obtained a WLLN (weak law of largenumbers) for the arrayfXni ;un i vn ;n 1g of random vari-ables under a Cesaro type condition, wherefun 1 ;n 1g andfvn + 1 ;n 1g are two sequences of integers. In this paper, weextend the result of Sung et al. [13] to a martingale typep Banachspace.
Sung, Soo-Hak,Hu, Tien-Chung,Volodin, Andrei I. Korean Mathematical Society 2006 대한수학회보 Vol.43 No.3
Sung et al. [13] obtained a WLLN (weak law of large numbers) for the array $\{X_{{ni},\;u_n{\leq}i{\leq}v_n,\;n{\leq}1\}$ of random variables under a Cesaro type condition, where $\{u_n{\geq}-{\infty},\;n{\geq}1\}$ and $\{v_n{\leq}+{\infty},\;n{\geq}1\}$ large two sequences of integers. In this paper, we extend the result of Sung et al. [13] to a martingale type p Banach space.
ON COMPLETE CONVERGENCE FOR ARRAYS OF ROWWISE INDEPENDENT RANDOM ELEMENTS
Sung Soo-Hak,Cabrera Manuel Ordonez,Hu Tien-Chung Korean Mathematical Society 2007 대한수학회지 Vol.44 No.2
A complete convergence theorem for arrays of rowwise independent random variables was proved by Sung, Volodin, and Hu [14]. In this paper, we extend this theorem to the Banach space without any geometric assumptions on the underlying Banach space. Our theorem also improves some known results from the literature.