Weak laws of large numbers for weighted independent random variables with infinite mean

2016 ◽  
Vol 109 ◽  
pp. 124-129 ◽  
Author(s):  
Toshio Nakata
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Weak Laws

scholarly journals A note on convergence of weighted sums of random variables

1985 ◽  
Vol 8 (4) ◽  
pp. 805-812 ◽  
Author(s):  
Xiang Chen Wang ◽  
M. Bhaskara Rao
Keyword(s):  
Integrability Condition ◽  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Uniform Integrability ◽  
Laws Of Large Numbers ◽  
Sums Of Random Variables ◽  
Large Numbers ◽  
Pairwise Independent Random Variables ◽  
Weak Laws

Under uniform integrability condition, some Weak Laws of large numbers are established for weighted sums of random variables generalizing results of Rohatgi, Pruitt and Khintchine. Some Strong Laws of Large Numbers are proved for weighted sums of pairwise independent random variables generalizing results of Jamison, Orey and Pruitt and Etemadi.

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.

Sign in / Sign up

Export Citation Format

Share Document