Abstract
The authors first present a Rosenthal inequality for sequence of extended negatively dependent (END) random variables. By means of the Rosenthal inequality, the authors obtain some complete moment convergence and mean convergence results for arrays of rowwise END random variables. The results in this paper extend and improve the corresponding theorems by Hu and Taylor (1997).
Highlights
The results in this paper extend and improve the corresponding theorems by Hu and Taylor (1997)
The concept of the complete convergence was introduced by Hsu and Robbins [1]
The goal of this paper is to study complete moment convergence and mean convergence for arrays of rowwise extended negatively dependent (END) random variables
Summary
The concept of the complete convergence was introduced by Hsu and Robbins [1]. A sequence of random variables {Un, n ≥ 1} is said to converge completely to a constant θ if ∞ ∑P (Un − θ > ε) < ∀ε > 0. (1) n=1. The authors first present a Rosenthal inequality for sequence of extended negatively dependent (END) random variables. By means of the Rosenthal inequality, the authors obtain some complete moment convergence and mean convergence results for arrays of rowwise END random variables.
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