A finitely additive version of the law of the iterated logarithm (Q2711186)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A finitely additive version of the law of the iterated logarithm |
scientific article |
Statements
6 May 2001
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finitely additive probability
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law of the iterated logarithm
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A finitely additive version of the law of the iterated logarithm (English)
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A finitely additive version of the law of the iterated logarithm (LIL) is proposed. At first, the authors describe the finitely additive setting and clarify the concept of stochastically independent random variables. Then they illustrate a version of the LIL which holds in the finitely additive setting. It is shown that in the case the probability P is a \(\sigma\)-additive probability measure, the classical version of the LIL is equivalent to their result. Finally, they give two examples in which the LIL fails, whereas the finitistic law being proposed is applicable.
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