The Law of the Iterated Logarithm

  • Allan Gut
Part of the Springer Texts in Statistics book series (STS, volume 75)


The central limit theorem tells us that suitably normalized sums can be approximated by a normal distribution. Although arbitrarily large values may occur, and will occur, one might try to bound the magnitude in some manner. This is what the law of the iterated logarithm (LIL) does, in that it provides a parabolic bound on how large the oscillations of the partial sums may be as a function of the number of summands.


Central Limit Theorem Iterate Logarithm Normal Random Variable Counting Process Finite Variance 
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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

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