Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 372390, 13 pages
doi:10.1155/2010/372390
Research Article

On Complete Convergence for Weighted Sums of φ-Mixing Random Variables

Wang Xuejun, Hu Shuhe, Yang Wenzhi, and Shen Yan

School of Mathematical Science, Anhui University, Hefei 230039, China

Received 4 February 2010; Revised 8 May 2010; Accepted 11 June 2010

Academic Editor: Andrei Volodin

Copyright © 2010 Wang Xuejun et al. 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

Some results on complete convergence for weighted sums ∑i=1naniXi are presented, where {Xn, n≥1} is a sequence of φ-mixing random variables and {ani,n≥1,i≥1} is an array of constants. They generalize the corresponding results for i.i.d sequence to the case of φ-mixing sequence.