Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences. (18th June 2012) - Wang, Xuejun; Hu, Shuhe; Yang, Wenzhi; Wang, Xinghui
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).