Abstract
In this paper, complete moment convergence for widely orthant dependent random variables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results extend recent results on complete convergence to complete moment convergence. These results on complete moment convergence are shown to yield new results on complete integral convergence.
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The authors are grateful to the referee for carefully reading the manuscript and for providing helpful comments and constructive criticism which enabled them to improve the paper.
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Supported by the National Natural Science Foundation of China (Grant Nos. 11671012, 11501004 and 11501005); the Natural Science Foundation of Anhui Province (Grant No. 1508085J06); the Key Projects for Academic Talent of Anhui Province (Grant No. gxbjZD2016005), and the Research Teaching Model Curriculum of Anhui University (Grant No. xjyjkc1407)
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Wu, Y., Wang, X.J. & Rosalsky, A. Complete Moment Convergence for Arrays of Rowwise Widely Orthant Dependent Random Variables. Acta. Math. Sin.-English Ser. 34, 1531–1548 (2018). https://doi.org/10.1007/s10114-018-7173-z
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DOI: https://doi.org/10.1007/s10114-018-7173-z
Keywords
- Complete convergence
- complete moment convergence
- array of widely orthant dependent random variables
- complete integral convergence