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Complete moment convergence and complete convergence for weighted sums of NSD random variables

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper, the equivalent conditions of complete moment convergence of the maximum partial weighted sums for negatively superadditive dependent (NSD) random variables are established without the assumption of identical distribution. As applications, the complete moment convergence, the complete convergence and strong law of large numbers for NSD random variables are obtained. The results obtained in the paper generalize or improve the corresponding ones for weighted sums of independent random variables and negatively associated random variables.

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Acknowledgments

The authors are most grateful to the Editor-in-Chief Manuel Lopez-Pellicer and two anonymous referees for careful reading of the manuscript and valuable suggestions which helped in improving an earlier version of this paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, People’s Republic of China

    Xin Deng, Xuejun Wang, Yi Wu & Yang Ding

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  1. Xin Deng
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  2. Xuejun Wang
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  3. Yi Wu
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  4. Yang Ding
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Correspondence to Xuejun Wang.

Additional information

Supported by the National Natural Science Foundation of China (11201001, 11171001, 11426032), the Natural Science Foundation of Anhui Province (1508085J06), the Research Teaching Model Curriculum of Anhui University (xjyjkc1407) and the Graduate Academic Innovation Research Project of Anhui University (yfc100025).

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Deng, X., Wang, X., Wu, Y. et al. Complete moment convergence and complete convergence for weighted sums of NSD random variables. RACSAM 110, 97–120 (2016). https://doi.org/10.1007/s13398-015-0225-7

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  • DOI: https://doi.org/10.1007/s13398-015-0225-7

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