On the strong laws of large numbers for weighted sums of random variables

2016 ◽  
Vol 118 ◽  
pp. 87-93 ◽  
Author(s):  
Pingyan Chen ◽  
Soo Hak Sung
Keyword(s):  
Random Variables ◽  
Weighted Sums ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Sums Of Random Variables ◽  
Large Numbers

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.

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.

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