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Convergence rates in the strong law of large numbers for martingale difference sequences. (English) Zbl 1253.60045
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 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)].

MSC:
60F15 Strong limit theorems
60G42 Martingales with discrete parameter
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