Some iterated logarithm results related to the central limit theorem.

Tomkins, R. J.

doi:10.1090/S0002-9947-1971-0275503-X

Some iterated logarithm results related to the central limit theorem.
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by R. J. Tomkins PDF

Trans. Amer. Math. Soc. 156 (1971), 185-192 Request permission

Abstract:

An iterated logarithm theorem is presented for sequences of independent, not necessarily bounded, random variables, the distribution of whose partial sums is related to the standard normal distribution in a particular manner. It is shown that if a sequence of independent random variables satisfies the Central Limit Theorem with a sufficiently rapid rate of convergence, then the law of the iterated logarithm holds. In particular, it is demonstrated that these results imply several known iterated logarithm results, including Kolmogorov’s celebrated theorem.

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Remarque sur la loi du logarithme itéré

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