Logarithmic averages of stable random variables are asymptotically normal (Q1805790)
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scientific article; zbMATH DE number 1364499
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Logarithmic averages of stable random variables are asymptotically normal |
scientific article; zbMATH DE number 1364499 |
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Logarithmic averages of stable random variables are asymptotically normal (English)
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18 November 1999
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The paper deals with almost sure central limit theorem for distributions in the domain of attraction of a stable law with the index \(\alpha \in (0,2)\). The paper contributes with the second order asymptotic. The difference between the logarithmic average and its limit a.s. is strongly approximated by a Wiener process. The rate of approximation is \(o((\log n)^{\delta})\) for each \(\delta >{5\over 12}\).
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stable distribution
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logarithmic average
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central limit theorem
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almost sure central limit theorem
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Wiener process
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