On the weak laws of large numbers for arrays of random variables

2009 ◽  
Vol 79 (23) ◽  
pp. 2405-2414 ◽  
Author(s):  
Yanjiao Meng ◽  
Zhengyan Lin
Keyword(s):  
Random Variables ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Weak Laws

scholarly journals Moderate Laws of Large Numbers via Weak Laws

2020 ◽  
Author(s):  
Yu-Lin Chou
Keyword(s):  
Law Of Large Numbers ◽  
Random Variables ◽  
Martingale Theory ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Weak Laws

By a $moderate$ $law$ $of$ $large$ $numbers$ we mean any theorem whose conclusion includes the $L^{p}$-vanishment of the sequence of the sample means of some centered random variables with $1 \leq p < +\infty$ given.Given any $1 \leq p < +\infty$ and any $\eps > 0$,we prove a moderate law of large numbers for $L^{p+\eps}$-bounded random variables that obey a weak law.Thus our moderate laws in particular complement those obtained from the martingale theory,and establish the counterintuitive fact that (for$L^{p+\eps}$-bounded random variables) where there is a weak law there is a moderate law.

THE CONVERGENCE AND WEAK LAWS OF LARGE NUMBERS FOR -MIXING RANDOM VARIABLES

2017 ◽  
Vol 58 (3-4) ◽  
pp. 455-463
Author(s):  
YAN-JIAO MENG
Keyword(s):  
Random Variables ◽  
Uniform Integrability ◽  
Type Condition ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Weak Laws ◽  
Mixing Random Variables

The $L_{r}$ convergence and a class of weak laws of large numbers are obtained for sequences of $\widetilde{\unicode[STIX]{x1D70C}}$-mixing random variables under the uniform Cesàro-type condition. This is weaker than the $p$th-order Cesàro uniform integrability.

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