Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 74634, 7 pages
doi:10.1155/2007/74634
Research Article
Convergence of Weighted Linear Process for ρ-Mixing Random Variables
Department of Mathematics and Statistics, Zhejiang Gongshang University, Hangzhou 310035, China
Received 10 April 2006; Revised 11 January 2007; Accepted 15 March 2007
Copyright © 2007 Guang-Hui Cai. 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
A central limit theorem and a functional central limit theorem are obtained for weighted linear process of ρ-mixing sequences for the Xt=∑i=0∞aiYt−i, where {Yi,0≤i<∞} is a sequence of ρ-mixing random variables with EYi=0,0<EYi2<∞,∑i=1∞ρ(2i)<∞. The results obtained generalize the results of Liang et al. (2004) to
ρ-mixing sequences.