Functional central limit theorem and log log law for multiplicative systems (Q1119262)
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scientific article; zbMATH DE number 4098399
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Functional central limit theorem and log log law for multiplicative systems |
scientific article; zbMATH DE number 4098399 |
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Functional central limit theorem and log log law for multiplicative systems (English)
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1988
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Let \(\{X_ n\}\) be a sequence of uniformly bounded random variables for which \[ E(X_{n_ 1}X_{n_ 2}...X_{n_ r})=0,\quad 1\leq n_ 1<n_ 2<...<n_ r,\quad r=1,2,..., \] \[ E((X^ 2_ n-1)(X^ 2_ m- 1))=0,\quad 1\leq m<n<\infty. \] The author proves that \(\{X_ n\}\) satisfies Donsker's functional central limit theorem and a weaker version of Strassen's law of iterated logarithm.
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multiplicative systems
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functional central limit theorem
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Strassen's law of iterated logarithm
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