On the Strong Convergence and Complete Convergence for Pairwise NQD Random Variables

Let an,n≥1 be a sequence of positive constants with an/n↑ and let X,Xn,n≥1 be a sequence of pairwise negatively quadrant dependent random variables. The complete convergence for pairwise negatively quadrant dependent random variables is studied under mild condition. In addition, the strong laws of l...

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Bibliographic Details
Main Authors: Aiting Shen, Ying Zhang, Andrei Volodin
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/949608
Description
Summary:Let an,n≥1 be a sequence of positive constants with an/n↑ and let X,Xn,n≥1 be a sequence of pairwise negatively quadrant dependent random variables. The complete convergence for pairwise negatively quadrant dependent random variables is studied under mild condition. In addition, the strong laws of large numbers for identically distributed pairwise negatively quadrant dependent random variables are established, which are equivalent to the mild condition ∑n=1∞PX>an<∞. Our results obtained in the paper generalize the corresponding ones for pairwise independent and identically distributed random variables.
ISSN:1085-3375
1687-0409