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Strong Law of Large Numbers Under a General Moment Condition

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Strong Law of Large Numbers Under a General Moment Condition
2.	Creator	Author's name, affiliation, country	Sergei Chobanyan; Georgian Academy of Sciences, Georgia
2.	Creator	Author's name, affiliation, country	Shlomo Levental; Michigan State University, USA
2.	Creator	Author's name, affiliation, country	Habib Salehi; Michigan State University, USA
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)
4.	Description	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2005-10-03
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1156
10.	Identifier	Digital Object Identifier	10.1214/ECP.v10-1156
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 10
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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