Journal of Theoretical Probability

, Volume 29, Issue 1, pp 32–47 | Cite as

Kolmogorov Type Law of the Logarithm for Arrays

  • Jørgen Hoffmann-Jørgensen
  • Yu Miao
  • Xiao Chun Li
  • Shou Fang Xu


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.


Kolmogorov’s law of the logarithm Independent random variables Bernstein’s inequality Kolmogorov’s inequality 

Mathematics Subject Classification



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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Jørgen Hoffmann-Jørgensen
    • 1
  • Yu Miao
    • 2
  • Xiao Chun Li
    • 2
  • Shou Fang Xu
    • 3
  1. 1.Department of MathematicsAarhus UniversityAarhusDenmark
  2. 2.College of Mathematics and Information ScienceHenan Normal UniversityXinxiang China
  3. 3.Department of Mathematics and Information ScienceXinxiang UniversityXinxiang China

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