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Complete convergence and complete moment convergence for martingale difference sequence

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Abstract

In the paper, we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale difference sequence. Especially, we get the Baum-Katz-type Theorem and Hsu-Robbins-type Theorem for martingale difference sequence. As an application, a strong law of large numbers for martingale difference sequence is obtained.

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Authors and Affiliations

  1. School of Mathematical Science, Anhui University, Hefei, 230601, P. R. China

    Xue Jun Wang & Shu He Hu

Authors
  1. Xue Jun Wang
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  2. Shu He Hu
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Correspondence to Xue Jun Wang.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 11201001, 11171001, 11126176 and 11226207), Natural Science Foundation of Anhui Province (Grant Nos. 1208085QA03 and 1308085QA03), Applied Teaching Model Curriculum of Anhui University (Grant No. XJYYXKC04), Students Innovative Training Project of Anhui University (Grant No. 201310357004), Doctoral Research Start-up Funds Projects of Anhui University and the Students Science Research Training Program of Anhui University (Grant No. KYXL2012007)

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Wang, X.J., Hu, S.H. Complete convergence and complete moment convergence for martingale difference sequence. Acta. Math. Sin.-English Ser. 30, 119–132 (2014). https://doi.org/10.1007/s10114-013-2243-8

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  • DOI: https://doi.org/10.1007/s10114-013-2243-8

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