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http://dx.doi.org/10.4134/BKMS.2006.43.3.543

ON THE WEAK LAWS WITH RANDOM INDICES FOR PARTIAL SUMS FOR ARRAYS OF RANDOM ELEMENTS IN MARTINGALE TYPE p BANACH SPACES  

Sung, Soo-Hak (Department of Applied Mathematics, Pai Chai University)
Hu, Tien-Chung (Department of Mathematics, National Tsing Hua University)
Volodin, Andrei I. (Department of Mathematics and Statistics, University of Regina)
Publication Information
Bulletin of the Korean Mathematical Society / v.43, no.3, 2006 , pp. 543-549 More about this Journal
Abstract
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.
Keywords
arrays of random elements; convergence in probability; martingale 쇼; e p Banach space; weak law of large numbers; randomly indexed sums; martingale difference sequence; Cesaro type condition;
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