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Equivalent conditions of complete moment and integral convergence for a class of dependent random variables

  • Yi Wu
  • Xuejun Wang
Original Paper
  • 80 Downloads

Abstract

Some equivalent conditions of complete moment and complete integral convergence for a class of dependent random variables are established. The results obtained in this paper extend the corresponding ones for negatively associated random variables. As applications, we present some results for specific sequences of random variables, such as \(\rho \)-mixing, \(\rho ^{*}\)-mixing, \(\varphi \)-mixing, \(\varphi ^{*}\)-mixing and m-dependent sequences.

Keywords

Complete moment convergence Complete integral convergence Convergence rate of tail probabilities Sums of identically distributed random variables 

Mathematics Subject Classification

60F15 

Notes

Acknowledgements

The authors are most grateful to the Editor-in-Chief Prof. Manuel López-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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Copyright information

© Springer-Verlag Italia 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesAnhui UniversityHefeiPeople’s Republic of China

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