A Finitely Additive Version of the Law of the Iterated Logarithm

A finitely additive version of the law of the iterated logarithm (LIL) is proposed. The formulation involves only finite-dimensional distributions of a sequence of independent random variables $(X_n)_{n\ge 1}$. It is also proved that in the case where one deals with $\sigma$-additive probabilities,...

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Bibliographic Details
Published in:Theory of probability and its applications 1999-01, Vol.44 (4), p.633-649
Main Authors: Epifani, I., Lijoi, A.
Format: Article
Language:English
Subjects:
Probability
Random variables
Theorems
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Summary:A finitely additive version of the law of the iterated logarithm (LIL) is proposed. The formulation involves only finite-dimensional distributions of a sequence of independent random variables $(X_n)_{n\ge 1}$. It is also proved that in the case where one deals with $\sigma$-additive probabilities, the given result is equivalent to the classical version of the LIL.
ISSN:0040-585X
1095-7219
DOI:10.1137/S0040585X97977884