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Journal of Applied Mathematics
Volume 2012, Article ID 104390, 10 pages
http://dx.doi.org/10.1155/2012/104390
Research Article

Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables

1College of Science, Guilin University of Technology, Guilin 541004, China
2Guangxi Key Laboratory of Spatial Information and Geomatics, Guilin University of Technology, Guilin 541004, China

Received 7 February 2012; Accepted 19 April 2012

Academic Editor: Martin Weiser

Copyright © 2012 Qunying Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The complete convergence for pairwise negative quadrant dependent (PNQD) random variables is studied. So far there has not been the general moment inequality for PNQD sequence, and therefore the study of the limit theory for PNQD sequence is very difficult and challenging. We establish a collection that contains relationship to overcome the difficulties that there is no general moment inequality. Sufficient and necessary conditions of complete convergence for weighted sums of PNQD random variables are obtained. Our results generalize and improve those on complete convergence theorems previously obtained by Baum and Katz (1965) and Wu (2002).