How to cite item

Strong Law of Large Numbers Under a General Moment Condition

   
@article{ECP1156,
	author = {Sergei Chobanyan and Shlomo Levental and Habib Salehi},
	title = {Strong Law of Large Numbers Under a General Moment Condition},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {10},
	year = {2005},
	keywords = {},
	abstract = {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.},
	pages = {no. 22, 218-222},
	issn = {1083-589X},
	doi = {10.1214/ECP.v10-1156},    
        url = {http://ecp.ejpecp.org/article/view/1156}}