Yongfeng Wu

Some mean convergence and complete convergence theorems for sequences of m-linearly negative quadrant dependent random variables

The structure of linearly negative quadrant dependent random variables is extended by introducing the structure of m-linearly negative quadrant dependent random variables (m = 1, 2, …). For a sequence of m-linearly negative quadrant dependent random variables {Xn, n ⩾ 1} and 1 < p < 2 (resp. 1 ⩽ p < 2), conditions are provided under which

A correction to\newline``Some mean convergence and complete convergence theorems for sequences of

n^{ - 1/p} \sum\limits_{k = 1}^n {\left( {\left. {X_k - } \right|EX_k } \right) \to } 0

-linearly negative quadrant dependent random variables''

in L1. Moreover, for 1 ⩽ p < 2, conditions are provided under which

Complete convergence and complete moment convergence for arrays of rowwise END random variables

n^{ - 1/p} \sum\limits_{k = 1}^n {\left( {X_k - EX_k } \right)}

On limiting behavior for arrays of rowwise negatively orthant dependent random variables

converges completely to 0. The current work extends some results of Pyke and Root (1968) and it extends and improves some results of Wu, Wang, and Wu (2006). An open problem is posed.

A note on the rates of convergence for weighted sums of ρ * -mixing random variables

ABSTRACT The authors study the complete moment convergence of weighted sums for arrays of rowwise negatively dependent random variables. The obtained results improve the corresponding results of Baek and Park (2010). Convergence of weighted sums for arrays of negatively dependent random variables and its applications. As an application, the authors obtain the complete moment convergence of linear processes based on pairwise negatively dependent random variables. In addition, the authors point out a gap of the proof in Baek and Park (2010) and raise an open problem.