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Equivalent conditions of complete convergence for weighted sums of ANA random variables

  • Haiwu Huang EMAIL logo
Published/Copyright: November 20, 2018
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Abstract

In this paper, the author investigates the complete convergence for weighted sums of asymptotically negatively associated (ANA) random variables with different distributions, and obtains some equivalent conditions of complete convergence theorem for weighted sums as well as summation of ANA cases. These results generalize and improve the corresponding ones obtained by Baum and Katz (1965), Peligrad and Gut (1999) and Cai (2006), respectively.

MSC 2010: 60F15

This paper is supported by the National Nature Science Foundation of China (11526085), the Humanities and Social Sciences Foundation for the Youth Scholars of Ministry of Education of China (15YJCZH066), the Science and Technology Plan Project of Hunan Province (2016TP1020) and the Construct Program of the Key Discipline in Hunan Province and the Science and Technology Plan project of Hengyang City (2017KJ183).


  1. (Communicated by Gejza Wimmer)

Acknowledgement

The author is most grateful to the Editor and the anonymous referees for carefully reading the paper and for offering valuable suggestions, which greatly improved this paper.

References

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Received: 2017-02-21
Accepted: 2017-07-10
Published Online: 2018-11-20
Published in Print: 2018-12-19

© 2018 Mathematical Institute Slovak Academy of Sciences

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