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On complete convergence and the strong law of large numbers for pairwise independent random variables

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Abstract

The complete convergence for the maximum partial sums of pairwise independent random variables is obtained. The Kolmogorov strong law of large numbers for pairwise i.i.d. random variables is also obtained. Similar results are established for the moving average processes of pairwise i.i.d. random variables and for pairwise independent random elements taking values in a Banach space.

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Authors and Affiliations

  1. Department of Statistics, Jinan University, Guangzhou, 510630, P.R. China

    P. Bai

  2. Department of Mathematics, Jinan University, Guangzhou, 510630, P.R. China

    P.-Y. Chen

  3. Department of Applied Mathematics, Pai Chai University, Taejon, 302-735, South Korea

    S. H. Sung

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  1. P. Bai
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  2. P.-Y. Chen
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  3. S. H. Sung
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Correspondence to S. H. Sung.

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Bai, P., Chen, PY. & Sung, S.H. On complete convergence and the strong law of large numbers for pairwise independent random variables. Acta Math Hung 142, 502–518 (2014). https://doi.org/10.1007/s10474-013-0370-4

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  • DOI: https://doi.org/10.1007/s10474-013-0370-4

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