Open AccessMoment Inequalities and Complete Moment Convergence
Author(s) -
SooHak Sung
Publication year - 2009
Publication title -
journal of inequalities and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 50
eISSN - 1029-242X
pISSN - 1025-5834
DOI - 10.1155/2009/271265
Subject(s) - mathematics , moment (physics) , convergence (economics) , inequality , mathematical analysis , calculus (dental) , physics , classical mechanics , economics , economic growth , medicine , dentistry
Let {Yi, 1≤i≤n} and {Zi, 1≤i≤n} be sequences of random variables. For any ϵ>0 and a>0, bounds for E(|∑i=1n(Yi+Zi)|−ϵa)+ and E(max1≤k≤n|∑i=1k(Yi+Zi)|−ϵa)+ are obtained. From these results, we establish general methods for obtaining the complete moment convergence. The results of Chow (1988), Zhu (2007), and Wu and Zhu (2009) are generalized and extended from independent (or dependent) random variables to random variables satisfying some mild conditions. Some applications to dependent random variables are discussed
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