Strong approximations of k-th records and k-th record times by Wiener processes (Q1090008)
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scientific article; zbMATH DE number 4007399
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Strong approximations of k-th records and k-th record times by Wiener processes |
scientific article; zbMATH DE number 4007399 |
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Strong approximations of k-th records and k-th record times by Wiener processes (English)
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1988
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We develop several strong approximations for k-th records and k-th record times by Wiener processes. Our main result is that it is possible to approximate by the same Wiener process up to the almost sure rate O(log j), where j stands for the index of the observations, the k-th records, the logarithms of the k-th record times, and the logarithms of the k-th inter-record times. We also prove some limiting weak laws and obtain Berry-Esséen-type theorems for k-th record times.
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strong approximations
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record times
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extreme values
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order statistics
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laws of large numbers
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law of the iterated logarithm
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invariance principles
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central limit theorem
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