Complete convergence of moving average process based on widely orthant dependent random variables

2016 ◽  
Vol 111 (3) ◽  
pp. 809-821
Author(s):  
Xinran Tao ◽  
Yi Wu ◽  
Hao Xia ◽  
Xuejun Wang
Keyword(s):  
Complete Convergence ◽  
Moving Average ◽  
Random Variables ◽  
Average Process ◽  
Moving Average Process ◽  
Dependent Random Variables ◽  
Widely Orthant Dependent

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 for weighted sums of widely orthant-dependent random variables

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Pingyan Chen ◽  
Soo Hak Sung
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Link Type ◽  
Convergence Results ◽  
Large Numbers ◽  
Widely Orthant Dependent

AbstractThe complete convergence results for weighted sums of widely orthant-dependent random variables are obtained. A strong law of large numbers for weighted sums of widely orthant-dependent random variables is also obtained. Our results extend and generalize some results of Chen and Sung (J. Inequal. Appl. 2018:121, 2018), Zhang et al. (J. Math. Inequal. 12:1063–1074, 2018), Chen and Sung (Stat. Probab. Lett. 154:108544, 2019), Lang et al. (Rev. Mat. Complut., 2020, 10.1007/s13163-020-00369-5), and Liang (Stat. Probab. Lett. 48:317–325, 2000).

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