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EQUIVALENT CONDITIONS OF COMPLETE MOMENT CONVERGENCE AND COMPLETE INTEGRAL CONVERGENCE FOR NOD SEQUENCES

  • Deng, Xin (School of Mathematical Sciences Anhui University) ;
  • Wang, Xuejun (School of Mathematical Sciences Anhui University)
  • Received : 2016.04.25
  • Published : 2017.05.31

Abstract

In this paper, seven equivalent conditions of complete moment convergence and complete integral convergence for negatively orthant dependent (NOD, in short) sequences are shown under two cases: identical distribution and stochastic domination. The results obtained in the paper improve and generalize the corresponding ones of Liang et al. [10]). In addition, an extension of the Baum-Katz complete convergence theorem: six equivalent conditions of complete convergence is established.

Acknowledgement

Supported by : National Natural Science Foundation of China, Natural Science Foundation of Anhui Province

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