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Kolmogorov Type Law of the Logarithm for Arrays

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Abstract

In this paper, we establish the analogue of Kolmogorov-type law of the logarithm for an array of independent random variables. The main methods are to develop the classic Bernstein’s and Kolmogorov’s inequality and replace the boundedness condition by conditions on the cumulant transform.

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Authors and Affiliations

  1. Department of Mathematics, Aarhus University, Aarhus, Denmark

    Jørgen Hoffmann-Jørgensen

  2. College of Mathematics and Information Science, Henan Normal University, Xinxiang , 453007, Henan Province, China

    Yu Miao & Xiao Chun Li

  3. Department of Mathematics and Information Science, Xinxiang University, Xinxiang , 453000, Henan Province, China

    Shou Fang Xu

Authors
  1. Jørgen Hoffmann-Jørgensen
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  2. Yu Miao
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  3. Xiao Chun Li
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  4. Shou Fang Xu
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Corresponding author

Correspondence to Yu Miao.

Additional information

This work is supported by NSFC (11001077, 11471104), NCET (NCET-11-0945), IRTSTHN (14IRTSTHN023), and Plan For Scientific Innovation Talent of Henan Province (124100510014).

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Hoffmann-Jørgensen, J., Miao, Y., Li, X.C. et al. Kolmogorov Type Law of the Logarithm for Arrays. J Theor Probab 29, 32–47 (2016). https://doi.org/10.1007/s10959-014-0574-8

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  • DOI: https://doi.org/10.1007/s10959-014-0574-8

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