scholarly journals Complete convergence and complete moment convergence for arrays of Rowwise asymptotically almost negatively associated random variables under the sub-linear expectations

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 633-644
Author(s):  
Dawei Lu ◽  
Jingyao Cong ◽  
Yanchun Yang
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Partial Sums ◽  
Complete Moment Convergence ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Moment Convergence ◽  
Negatively Associated Random Variables ◽  
Asymptotically Almost Negatively Associated

In this article, we investigate the complete convergence and complete moment convergence for maximal partial sums of asymptotically almost negatively associated random variables under the sublinear expectations. The results obtained in the article are the extensions of the complete convergence and complete moment convergence under classical linear expectation space.

scholarly journals Complete Convergence for Arrays of Rowwise Asymptotically Almost Negatively Associated Random Variables

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Xuejun Wang ◽  
Shuhe Hu ◽  
Wenzhi Yang
Keyword(s):  
Complete Convergence ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Weighted Sums ◽  
Strong Law ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Negatively Associated Random Variables ◽  
Large Numbers ◽  
Asymptotically Almost Negatively Associated

Let{Xni,i≥1,n≥1}be an array of rowwise asymptotically almost negatively associated random variables. Some sufficient conditions for complete convergence for arrays of rowwise asymptotically almost negatively associated random variables are presented without assumptions of identical distribution. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of asymptotically almost negatively associated random variables is obtained.

scholarly journals On Complete Moment Convergence of Weighted Sums for Arrays of Rowwise Negatively Associated Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Mingle Guo ◽  
Dongjin Zhu
Keyword(s):  
Moving Average ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Moment Convergence ◽  
Negatively Associated Random Variables ◽  
Moving Average Processes

The complete moment convergence of weighted sums for arrays of rowwise negatively associated random variables is investigated. Some sufficient conditions for complete moment convergence of weighted sums for arrays of rowwise negatively associated random variables are established. Moreover, the results of Baek et al. (2008), are complemented. As an application, the complete moment convergence of moving average processes based on a negatively associated random sequences is obtained, which improves the result of Li et al. (2004).

scholarly journals On Complete Convergence of Moving Average Process for AANA Sequence

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Wenzhi Yang ◽  
Xuejun Wang ◽  
Nengxiang Ling ◽  
Shuhe Hu
Keyword(s):  
Complete Convergence ◽  
Moving Average ◽  
Random Variables ◽  
Partial Sums ◽  
Complete Moment Convergence ◽  
Average Process ◽  
Moving Average Process ◽  
Moment Convergence ◽  
The Moment ◽  
Asymptotically Almost Negatively Associated

We investigate the moving average process such thatXn=∑i=1∞aiYi+n,n≥1, where∑i=1∞|ai|<∞and{Yi,1≤i<∞}is a sequence of asymptotically almost negatively associated (AANA) random variables. The complete convergence, complete moment convergence, and the existence of the moment of supermum of normed partial sums are presented for this moving average process.

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