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

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.

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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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Authors and Affiliations

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

    Yi Wu & Xuejun Wang

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  1. Yi Wu
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  2. Xuejun Wang
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Correspondence to Xuejun Wang.

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Supported by the National Natural Science Foundation of China (11671012, 11501004, 11501005), the Natural Science Foundation of Anhui Province (1508085J06) and the Key Projects for Academic Talent of Anhui Province (gxbjZD2016005).

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Wu, Y., Wang, X. Equivalent conditions of complete moment and integral convergence for a class of dependent random variables. RACSAM 112, 575–592 (2018). https://doi.org/10.1007/s13398-017-0399-2

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  • DOI: https://doi.org/10.1007/s13398-017-0399-2

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