Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 838301, 11 pages
doi:10.1155/2010/838301
Research Article

Doob's Type Inequality and Strong Law of Large Numbers for Demimartingales

Wang Xuejun, Hu Shuhe, Zhao Ting, and Yang Wenzhi

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

Received 9 October 2009; Revised 14 December 2009; Accepted 28 January 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

We establish some maximal inequalities for demimartingales which generalize the result of Wang (2004). The maximal inequality for demimartingales is used as a key inequality to establish other results including Doob's type maximal inequality, strong law of large numbers, strong growth rate, and integrability of supremum for demimartingales, which generalize and improve partial results of Christofides (2000) and Prakasa Rao (2007).