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Abstract and Applied Analysis
Volume 2012, Article ID 572493, 13 pages
http://dx.doi.org/10.1155/2012/572493
Research Article

Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences

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

Received 31 May 2012; Accepted 14 June 2012

Academic Editor: Sung Guen Kim

Copyright © 2012 Xuejun Wang 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 study the complete convergence and complete moment convergence for martingale difference sequence. Especially, we get the Baum-Katz-type Theorem and Hsu-Robbins-type Theorem for martingale difference sequence. As a result, the Marcinkiewicz-Zygmund strong law of large numbers for martingale difference sequence is obtained. Our results generalize the corresponding ones of Stoica (2007, 2011).