Summen unabhängiger Zufallsvariablen, die durch die Maximalterme dominiert werden. (Sums of independent random variables which are dominated by maximal terms) (Q808086)
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scientific article; zbMATH DE number 4209206
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Summen unabhängiger Zufallsvariablen, die durch die Maximalterme dominiert werden. (Sums of independent random variables which are dominated by maximal terms) |
scientific article; zbMATH DE number 4209206 |
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Summen unabhängiger Zufallsvariablen, die durch die Maximalterme dominiert werden. (Sums of independent random variables which are dominated by maximal terms) (English)
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1990
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The author shows for i.i.d. random variables \(X_ i\) with a symmetric distribution function F that \[ (*)\;\limsup | X_ n| /(\max_{1\leq i\leq n-1}| S_ i|)=\infty \] if and only if \(EX^ 2_ 1=\infty\). In the other extreme case of positive random variables, an old result of Kesten states the equivalence of (*) with the non- existence of the first moment.
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random walk
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maximal terms
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non-existence of the first moment
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