A uniform central limit theorem for nonuniform \(\phi\)-mixing random fields (Q1176151)
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scientific article; zbMATH DE number 13533
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A uniform central limit theorem for nonuniform \(\phi\)-mixing random fields |
scientific article; zbMATH DE number 13533 |
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A uniform central limit theorem for nonuniform \(\phi\)-mixing random fields (English)
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25 June 1992
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Partial sums of strictly stationary random fields on \(Z^ d\) are analyzed under the non-uniform version of the so-called \(\phi\)-mixing condition and, under some additional assumptions, are shown to converge to the Brownian motion. \textit{R. C. Bradley} [Stat. Probab. Lett. 8, No. 5, 489-491 (1989; Zbl 0697.60054)]\ indicates that for \(d>1\) only such non-uniform version of the \(\phi\)-mixing condition can lead to non- trivial limit theorems.
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strictly stationary random fields
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\(\phi\)-mixing condition
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limit theorems
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