scholarly journals The Hájek-Rényi-Chow maximal inequality and a strong law of large numbers in Riesz spaces

2020 ◽  
Vol 481 (1) ◽  
pp. 123462
Author(s):  
Wen-Chi Kuo ◽  
David F. Rodda ◽  
Bruce A. Watson
Keyword(s):  
Law Of Large Numbers ◽  
Maximal Inequality ◽  
Strong Law ◽  
Riesz Spaces ◽  
Large Numbers

scholarly journals Ergodic theory and the Strong Law of Large Numbers on Riesz spaces

2007 ◽  
Vol 325 (1) ◽  
pp. 422-437 ◽  
Author(s):  
Wen-Chi Kuo ◽  
Coenraad C.A. Labuschagne ◽  
Bruce A. Watson
Keyword(s):  
Ergodic Theory ◽  
Law Of Large Numbers ◽  
Strong Law ◽  
Riesz Spaces ◽  
Large Numbers

scholarly journals On Strong Convergence for Weighted Sums of a Class of Random Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Aiting Shen
Keyword(s):  
Strong Convergence ◽  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Maximal Inequality ◽  
Weighted Sums ◽  
Moment Condition ◽  
Strong Law ◽  
Linear Statistics ◽  
Large Numbers

Let{Xn,n≥1}be a sequence of random variables satisfying the Rosenthal-type maximal inequality. Complete convergence is studied for linear statistics that are weighted sums of identically distributed random variables under a suitable moment condition. As an application, the Marcinkiewicz-Zygmund-type strong law of large numbers is obtained. Our result generalizes the corresponding one of Zhou et al. (2011) and improves the corresponding one of Wang et al. (2011, 2012).

scholarly journals On Some Conditions for Strong Law of Large Numbers for Weighted Sums of END Random Variables under Sublinear Expectations

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Xiaochen Ma ◽  
Qunying Wu
Keyword(s):  
Probability Space ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Sublinear Expectation ◽  
Negatively Dependent Random Variables ◽  
Large Numbers ◽  
End Random Variables

In this article, we research some conditions for strong law of large numbers (SLLNs) for weighted sums of extended negatively dependent (END) random variables under sublinear expectation space. Our consequences contain the Kolmogorov strong law of large numbers and the Marcinkiewicz strong law of large numbers for weighted sums of extended negatively dependent random variables. Furthermore, our results extend strong law of large numbers for some sequences of random variables from the traditional probability space to the sublinear expectation space context.

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