On the law of the iterated logarithm

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On the law of the iterated logarithm.

The law of the iterated logarithm provides a family of bounds all of the same order such that with probability one only finitely many partial sums of a sequence of independent and identically distributed random variables exceed some members of the family, while for others infinitely many do so. In the former case, the total number of such excesses has therefore a proper probability distribution...

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In this paper, we first discuss the history of the law of the iterated logarithm. We then focus our discussion on how it was introduced in analysis. Finally we mention different types of law of the iterated logarithm and state some of the recent developments. In order to discuss the history and developments of law of the iterated logarithm, some definitions and theorems are in order: Definition...

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The law of the iterated logarithm for LNQD sequences

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ژورنال

عنوان ژورنال: Journal of Multivariate Analysis

سال: 1981

ISSN: 0047-259X

DOI: 10.1016/0047-259x(81)90080-4