Complete convergence and strong laws of large numbers for weighted sums of negatively orthant dependent random variables

2015 ◽  
Vol 148 (1) ◽  
pp. 83-95 ◽  
Author(s):  
P. Chen ◽  
S. H. Sung
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers

scholarly journals On exact strong laws of large numbers under general dependence conditions

2018 ◽  
Vol 38 (1) ◽  
pp. 103-121 ◽  
Author(s):  
André Adler ◽  
Przemysław Matuła
Keyword(s):  
Random Variables ◽  
Almost Sure Convergence ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Laws Of Large Numbers ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Strong Laws ◽  
Large Numbers ◽  
Dependence Conditions

We study the almost sure convergence of weighted sums of dependent random variables to a positive and finite constant, in the case when the random variables have either mean zero or no mean at all. These are not typical strong laws and they are called exact strong laws of large numbers. We do not assume any particular type of dependence and furthermore consider sequences which are not necessarily identically distributed. The obtained results may be applied to sequences of negatively associated random variables.

scholarly journals COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF SEQUENCES OF AANA RANDOM VARIABLES

2008 ◽  
Vol 50 (3) ◽  
pp. 351-357 ◽  
Author(s):  
GUANG-HUI CAI ◽  
BAO-CAI GUO
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Rocky Mountain ◽  
Weighted Sums ◽  
Laws Of Large Numbers ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Strong Laws ◽  
Large Numbers ◽  
Asymptotically Almost Negatively Associated

AbstractLet Xn, n ≥ 1 be an asymptotically almost negatively associated (AANA) sequence of random variables. Some complete convergence and Marcinkiewicz–Zygmund type strong laws of large numbers for an AANA sequence of random variables are obtained. The results obtained generalize the results of Kim, Ko and Lee (Kim, T. S., Ko, M. H. and Lee, I. H. 2004. On the strong laws for asymptotically almost negatively associated random variables. Rocky Mountain J. of Math. 34, 979–989.).

scholarly journals On the Strong Convergence and Complete Convergence for Pairwise NQD Random Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Aiting Shen ◽  
Ying Zhang ◽  
Andrei Volodin
Keyword(s):  
Strong Convergence ◽  
Mild Condition ◽  
Complete Convergence ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Independent And Identically Distributed

Letan,n≥1be a sequence of positive constants withan/n↑and letX,Xn,n≥1be a sequence of pairwise negatively quadrant dependent random variables. The complete convergence for pairwise negatively quadrant dependent random variables is studied under mild condition. In addition, the strong laws of large numbers for identically distributed pairwise negatively quadrant dependent random variables are established, which are equivalent to the mild condition∑n=1∞PX>an<∞. Our results obtained in the paper generalize the corresponding ones for pairwise independent and identically distributed random variables.

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 laws of large numbers for weighted sums of $$\tilde \rho $$ -mixing random variables

2007 ◽  
Vol 57 (4) ◽  
Author(s):  
Guang-hui Cai
Keyword(s):  
Random Sample ◽  
Random Variables ◽  
Weighted Sums ◽  
Laws Of Large Numbers ◽  
Linear Statistics ◽  
Strong Laws ◽  
Large Numbers ◽  
Mixing Random Variables

AbstractStrong laws are established for linear statistics that are weighted sums of a $$\tilde \rho $$ -mixing random sample. The results obtained generalize the results of Baxter et al. [SLLN for weighted independent indentically distributed random variables, J. Theoret. Probab. 17 (2004), 165–181] to $$\tilde \rho $$ -mixing random variables.

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