Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 379743, 12 pages
doi:10.1155/2009/379743
Research Article

Moment Inequality for φ-Mixing Sequences and Its Applications

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

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

Received 11 April 2009; Accepted 21 September 2009

Academic Editor: Sever Silvestru Dragomir

Copyright © 2009 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

Firstly, the maximal inequality for φ-mixing sequences is given. By using the maximal inequality, we study the convergence properties for φ-mixing sequences. The Hájek-Rényi-type inequality, strong law of large numbers, strong growth rate and the integrability of supremum for φ-mixing sequences are obtained.