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 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 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.

Complete moment convergence of moving average processes under ρ-mixing assumption

2011 ◽  
Vol 61 (6) ◽  
Author(s):  
Xing-Cai Zhou ◽  
Jin-Guan Lin
Keyword(s):  
Infinite Sequence ◽  
Moving Average ◽  
Random Variables ◽  
Partial Sums ◽  
Complete Moment Convergence ◽  
Real Numbers ◽  
Moment Convergence ◽  
Summable Sequence ◽  
Moving Average Processes ◽  
Mixing Random Variables

AbstractLet {Y i: −∞ < i < ∞} be a doubly infinite sequence of identically distributed ρ-mixing random variables, and {a i: −∞ < i < ∞} an absolutely summable sequence of real numbers. In this paper we prove the complete moment convergence for the partial sums of moving average processes $\{ X_n = \sum\limits_{i = - \infty }^\infty {a_i Y_{i + n,} n \geqslant 1} \} $ based on the sequence {Y i: −∞ < i < ∞} of ρ-mixing random variables under some suitable conditions.

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