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Some convergence properties for the maximum of partial sums of m-negatively associated random variables

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Abstract

In this paper, we present the Spitzer type law of large numbers for the maximum of partial sums of m-negatively associated random variables \(\left\{ X_n,n\ge 1\right\} \) and the \(L_p\) convergence property under the Cesàro uniform integrability condition for the maximum of partial sums. In addition, we give some simulations to verify the convergence behavior of \(\frac{1}{\psi (n)}\sum _{i=1}^{n}X_i\) which is in accordance with our theoretical result. The main results obtained in this paper extend and improve the corresponding ones for negatively associated random variables.

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Acknowledgements

The authors are most grateful to the Editor and anonymous referee for carefully reading the manuscript and for 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

    Mengge Wang & Xuejun Wang

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  1. Mengge Wang
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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), the Natural Science Foundation of Anhui Province (1508085J06), the Key Projects for Academic Talent of Anhui Province (gxbjZD2016005), the Project on Reserve Candidates for Academic and Technical Leaders of Anhui Province (2017H123) and the Students Innovative Training Project of Anhui University (201710357205).

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Wang, M., Wang, X. Some convergence properties for the maximum of partial sums of m-negatively associated random variables. RACSAM 113, 2345–2358 (2019). https://doi.org/10.1007/s13398-019-00626-3

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  • DOI: https://doi.org/10.1007/s13398-019-00626-3

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