Block records and maxima of the increments of the Wiener process (Q1973291)
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scientific article; zbMATH DE number 1436935
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Block records and maxima of the increments of the Wiener process |
scientific article; zbMATH DE number 1436935 |
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Block records and maxima of the increments of the Wiener process (English)
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23 May 2002
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Let \(\{W(t), t\geq 0\}\), \(W(0)=0,\) be the Wiener process. The basic result of this paper consists in proving that there exists a r.v. \(N\) and a sequence \(\{Z_n \}\) of i.i.d. random variables such that a.s. for \(N\geq n\) the following equality is true \[ \max_{0\leq t\leq n}(W(t)-W(t+1))=\max(Z_1,\ldots ,Z_n). \]
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increments of Wiener process
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block record
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l-dependent sequences
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