scholarly journals Complete Moment Convergence of Weighted Sums for Arrays of Rowwiseφ-Mixing Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Ming Le Guo
Keyword(s):  
Moving Average ◽  
Random Sequence ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Moment Inequality ◽  
Moment Convergence ◽  
Moving Average Processes ◽  
Mixing Random Variables

The complete moment convergence of weighted sums for arrays of rowwiseφ-mixing random variables is investigated. By using moment inequality and truncation method, the sufficient conditions for complete moment convergence of weighted sums for arrays of rowwiseφ-mixing random variables are obtained. The results of Ahmed et al. (2002) are complemented. As an application, the complete moment convergence of moving average processes based on aφ-mixing random sequence is obtained, which improves the result of Kim et al. (2008).

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).

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.

Complete moment convergence forweighted sums of pairwise negatively quadrant dependent random variables

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3459-3471
Author(s):  
Mingming Zhao ◽  
Shengnan Ding ◽  
Di Zhang ◽  
Xuejun Wang
Keyword(s):  
Theoretical Result ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Dependent Random Variables ◽  
Moment Convergence

In this article, the complete moment convergence for weighted sums of pairwise negatively quadrant dependent (NQD, for short) random variables is studied. Several sufficient conditions to prove the complete moment convergence for weighted sums of NQD random variables are presented. The results obtained in the paper extend some corresponding ones in the literature. The simulation is also presented which can verify the validity of the theoretical result.

scholarly journals Complete moment convergence of moving average processes for m-WOD sequence

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lihong Guan ◽  
Yushan Xiao ◽  
Yanan Zhao
Keyword(s):  
Moving Average ◽  
Random Variables ◽  
Random Variable ◽  
Complete Moment Convergence ◽  
Real Numbers ◽  
Mild Conditions ◽  
Moment Convergence ◽  
Summable Sequence ◽  
Moving Average Processes ◽  
Widely Orthant Dependent

AbstractIn this paper, the complete moment convergence for the partial sum of moving average processes $\{X_{n}=\sum_{i=-\infty }^{\infty }a_{i}Y_{i+n},n\geq 1\}$ { X n = ∑ i = − ∞ ∞ a i Y i + n , n ≥ 1 } is established under some mild conditions, where $\{Y_{i},-\infty < i<\infty \}$ { Y i , − ∞ < i < ∞ } is a sequence of m-widely orthant dependent (m-WOD, for short) random variables which is stochastically dominated by a random variable Y, and $\{a_{i},-\infty < i<\infty \}$ { a i , − ∞ < i < ∞ } is an absolutely summable sequence of real numbers. These conclusions promote and improve the corresponding results from m-extended negatively dependent (m-END, for short) sequences to m-WOD sequences.

scholarly journals Complete moment convergence for Sung’s type weighted sums of ρ*-mixing random variables

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1447-1453 ◽  
Author(s):  
Wei Li ◽  
Pingyan Chen ◽  
Soo Sung
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Convergence Result ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Moment Convergence ◽  
Mixing Random Variables

In this paper, the authors study a complete moment convergence result for Sung?s type weighted sums of ?*-mixing random variables. This result extends and improves the corresponding theorem of Sung [S.H. Sung, Complete convergence for weighted sums of ?*-mixing random variables, Discrete Dyn. Nat. Soc. 2010 (2010), Article ID 630608, 13 pages].

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