Studentized increments of partial sums (Q1326987)
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scientific article; zbMATH DE number 589842
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Studentized increments of partial sums |
scientific article; zbMATH DE number 589842 |
Statements
Studentized increments of partial sums (English)
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15 December 1994
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Let \(X, X_ 1, X_ 2,\dots\) be i.i.d. random variables with \(EX=0\). Assuming a necessary and sufficient condition for \(X\) to belong to the domain of attraction of the normal law, i.e. \[ \lim_{x\to\infty} (x^ 2 P(| X|> x)/ E X^ 2 I(| X| \leq x)) =0, \] the authors study almost sure limiting properties of Studentized increments of partial sums \(S_ n= \sum_{i=1}^ n X_ i\).
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domain of attraction of the normal law
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almost sure limiting properties of Studentized increments of partial sums
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