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. It is also proved that in the case where one deals with σ-additive probabilities, the given result is equivalent to the classical version of the LIL.
A finitely additive version of the law of the iterated logarithm
LIJOI, ANTONIO
1999
Abstract
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. It is also proved that in the case where one deals with σ-additive probabilities, the given result is equivalent to the classical version of the LIL.
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