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ON COMPLETE CONVERGENCE AND COMPLETE MOMENT CONVERGENCE FOR A CLASS OF RANDOM VARIABLES

  • Wang, Xuejun ;
  • Wu, Yi
  • Received : 2016.04.25
  • Published : 2017.05.01

Abstract

In this paper, the complete convergence and complete moment convergence for a class of random variables satisfying the Rosenthal type inequality are investigated. The sufficient and necessary conditions for the complete convergence and complete moment convergence are provided. As applications, the Baum-Katz type result and the Marcinkiewicz-Zygmund type strong law of large numbers for a class of random variables satisfying the Rosenthal type inequality are established. The results obtained in the paper extend the corresponding ones for some dependent random variables.

Keywords

complete convergence;complete moment convergence;stochastic domination;Rosenthal type inequality

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Cited by

  1. Complete convergence and complete moment convergence for weighted sums of extended negatively dependent random variables under sub-linear expectation vol.2017, pp.1, 2017, https://doi.org/10.1186/s13660-017-1538-1
  2. Sufficient and necessary conditions of complete convergence for asymptotically negatively associated random variables vol.2018, pp.1, 2018, https://doi.org/10.1186/s13660-018-1906-5
  3. Equivalent conditions of the complete convergence for weighted sums of NSD random variables pp.1532-415X, 2018, https://doi.org/10.1080/03610926.2018.1500601
  4. Some Types of Convergence for Negatively Dependent Random Variables under Sublinear Expectations vol.2019, pp.1607-887X, 2019, https://doi.org/10.1155/2019/9037258

Acknowledgement

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