Convergence rates in the strong law of large numbers for martingale difference sequences (Q448737)

Summary: 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 \textit{G. Stoica} [J. Math. Anal. Appl. 336, No. 2, 1489--1492 (2007; Zbl 1130.60020); J. Math. Anal. Appl. 381, No. 2, 910--913 (2011; Zbl 1237.60025)].