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Exponential inequalities for associated random variables and strong laws of large numbers

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Abstract

Some exponential inequalities for partial sums of associated random variables are established. These inequalities improve the corresponding results obtained by Ioannides and Roussas (1999), and Oliveira (2005). As application, some strong laws of large numbers are given. For the case of geometrically decreasing covariances, we obtain the rate of convergence n −1/2(log log n)1/2(log n) which is close to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Ioannides and Roussas (1999), and Oliveira (2005) only got n −1/3(log n)2/3 and n −1/3(log n)5/3, separately.

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Authors and Affiliations

  1. Deptartment of Mathematics, Guangxi Normal University, Guilin, 541004, China

    Shan-chao Yang

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Min Chen

Authors
  1. Shan-chao Yang
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  2. Min Chen
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Correspondence to Min Chen.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 10161004, 70221001, 70331001) and the Natural Science Foundation of Guangxi Province of China (Grant No. 04047033)

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Yang, Sc., Chen, M. Exponential inequalities for associated random variables and strong laws of large numbers. SCI CHINA SER A 50, 705–714 (2007). https://doi.org/10.1007/s11425-007-0026-3

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  • DOI: https://doi.org/10.1007/s11425-007-0026-3

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