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Journal of Applied Mathematics
Volume 2014, Article ID 612140, 8 pages
http://dx.doi.org/10.1155/2014/612140
Research Article

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

1School of Economics and Management, Fuyang Normal College, Fuyang 236037, China
2School of Economics and Management, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received 12 November 2013; Revised 23 January 2014; Accepted 11 February 2014; Published 19 March 2014

Academic Editor: Fernando Simões

Copyright © 2014 Chongfeng Lan. 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 equivalent conditions of complete convergence are established for weighted sums of -mixing random variables with different distributions. Our results extend and improve the Baum and Katz complete convergence theorem. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequence of -mixing random variables is obtained.