scholarly journals Complete Convergence for Moving Average Process of Martingale Differences

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Wenzhi Yang ◽  
Shuhe Hu ◽  
Xuejun Wang
Keyword(s):  
Complete Convergence ◽  
Moving Average ◽  
Random Variables ◽  
Complete Moment Convergence ◽  
Average Process ◽  
Moving Average Process ◽  
Martingale Differences ◽  
Moment Convergence ◽  
Moving Process

Under some simple conditions, by using some techniques such as truncated method for random variables (see e.g., Gut (2005)) and properties of martingale differences, we studied the moving process based on martingale differences and obtained complete convergence and complete moment convergence for this moving process. Our results extend some related ones.

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.

scholarly journals Complete convergence and complete moment convergence for negatively dependent random variables under sub-linear expectations

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1093-1104
Author(s):  
Qunying Wu ◽  
Yuanying Jiang
Keyword(s):  
Probability Space ◽  
Complete Convergence ◽  
Random Variables ◽  
Complete Moment Convergence ◽  
Convergence Theorems ◽  
Dependent Random Variables ◽  
Moment Convergence ◽  
Negatively Dependent Random Variables

This paper we study and establish the complete convergence and complete moment convergence theorems under a sub-linear expectation space. As applications, the complete convergence and complete moment convergence for negatively dependent random variables with CV (exp (ln? |X|)) < ?, ? > 1 have been generalized to the sub-linear expectation space context. We extend some complete convergence and complete moment convergence theorems for the traditional probability space to the sub-linear expectation space. Our results generalize corresponding results obtained by Gut and Stadtm?ller (2011), Qiu and Chen (2014) and Wu and Jiang (2016). There is no report on the complete moment convergence under sub-linear expectation, and we provide the method to study this subject.

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