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2005 Strong Law of Large Numbers Under a General Moment Condition
Sergei Chobanyan, Shlomo Levental, Habib Salehi
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Electron. Commun. Probab. 10: 218-222 (2005). DOI: 10.1214/ECP.v10-1156


We use our maximum inequality for $p$-th order random variables ($p>1$) to prove a strong law of large numbers (SLLN) for sequences of $p$-th order random variables. In particular, in the case $p=2$ our result shows that $\sum f(k)/k < \infty$ is a sufficient condition for SLLN for $f$-quasi-stationary sequences. It was known that the above condition, under the additional assumption of monotonicity of $f$, implies SLLN (Erdos (1949), Gal and Koksma (1950), Gaposhkin (1977), Moricz (1977)). Besides getting rid of the monotonicity condition, the inequality enables us to extend thegeneral result to $p$-th order random variables, as well as to the case of Banach-space-valued random variables.


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Sergei Chobanyan. Shlomo Levental. Habib Salehi. "Strong Law of Large Numbers Under a General Moment Condition." Electron. Commun. Probab. 10 218 - 222, 2005.


Accepted: 3 October 2005; Published: 2005
First available in Project Euclid: 4 June 2016

zbMATH: 1112.60024
MathSciNet: MR2175402
Digital Object Identifier: 10.1214/ECP.v10-1156

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