Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 863931, 24 pages
http://dx.doi.org/10.1155/2012/863931
Research Article

On Complete Convergence of Moving Average Process for AANA Sequence

Wenzhi Yang,1 Xuejun Wang,1 Nengxiang Ling,2 and Shuhe Hu1

1School of Mathematical Science, Anhui University, Hefei 230039, China
2School of Mathematics, Hefei University of Technology, Hefei 230009, China

Received 23 November 2011; Accepted 28 February 2012

Academic Editor: Cengiz Çinar

Copyright © 2012 Wenzhi Yang 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

We investigate the moving average process such that Xn=∑i=1∞aiYi+n, n≥1, where ∑i=1∞|ai|<∞ and {Yi, 1≤i<∞} is a sequence of asymptotically almost negatively associated (AANA) random variables. The complete convergence, complete moment convergence, and the existence of the moment of supermum of normed partial sums are presented for this moving average process.