scholarly journals Strong convergence for m-pairwise negatively quadrant dependent random variables

2015 ◽  
Vol 50 (1) ◽  
pp. 245-259 ◽  
Author(s):  
Yongfeng Wu ◽  
◽  
Andrew Rosalsky ◽  
Keyword(s):  
Strong Convergence ◽  
Random Variables ◽  
Dependent Random Variables

scholarly journals A Note on the Rate of Strong Convergence for Weighted Sums of Arrays of Rowwise Negatively Orthant Dependent Random Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Qingxia Zhang ◽  
Dingcheng Wang
Keyword(s):  
Strong Convergence ◽  
Open Problem ◽  
Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables

Let{Xni;i≥1,n≥1}be an array of rowwise negatively orthant dependent (NOD) random variables. The authors discuss the rate of strong convergence for weighted sums of arrays of rowwise NOD random variables and solve an open problem posed by Huang and Wang (2012).

scholarly journals Strong Laws of Large Numbers for Arrays of Rowwise NA and LNQD Random Variables

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Jiangfeng Wang ◽  
Qunying Wu
Keyword(s):  
Strong Convergence ◽  
Random Variables ◽  
Convergence Properties ◽  
Dependent Random Variables ◽  
Laws Of Large Numbers ◽  
Negatively Associated ◽  
Strong Laws ◽  
Large Numbers

Some strong laws of large numbers and strong convergence properties for arrays of rowwise negatively associated and linearly negative quadrant dependent random variables are obtained. The results obtained not only generalize the result of Hu and Taylor to negatively associated and linearly negative quadrant dependent random variables, but also improve it.

Strong convergence properties for arrays of rowwise negatively orthant dependent random variables

2017 ◽  
Vol 67 (1) ◽  
pp. 235-244
Author(s):  
Aiting Shen ◽  
Yu Zhang ◽  
Andrei Volodin
Keyword(s):  
Strong Convergence ◽  
Complete Convergence ◽  
Random Variables ◽  
Random Variable ◽  
Convergence Properties ◽  
Exponential Moment ◽  
Dependent Random Variables

Abstract Let {Xni , i ≥ 1, n ≥1} be an array of rowwise negatively orthant dependent random variables which is stochastically dominated by a random variable X. Wang et al. [15. Complete convergence for arrays of rowwise negatively orthant dependent random variables, RACSAM, 106 (2012), 235–245] studied the complete convergence for arrays of rowwise negatively orthant dependent random variables under the condition that X has an exponential moment, which seems too strong. We will further study the complete convergence for arrays of rowwise negatively orthant dependent random variables under the condition that X has a moment, which is weaker than exponential moment. Our results improve the corresponding ones of Wang et al. [15].

scholarly journals A Note on Strong Convergence of Sums of Dependent Random Variables

2009 ◽  
Vol 2009 ◽  
pp. 1-7
Author(s):  
Tien-Chung Hu ◽  
Neville C. Weber
Keyword(s):  
Strong Convergence ◽  
Random Variables ◽  
Dependent Random Variables

For a sequence of dependent square-integrable random variables and a sequence of positive constants{bn,  n≥1}, conditions are provided under which the series∑i=1n(Xi−EXi)/biconverges almost surely asn→∞. These conditions are weaker than those provided by Hu et al. (2008).

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