The almost sure central limit theorems for certain order statistics of some stationary Gaussian sequences
The almost sure central limit theorems for certain order statistics of some stationary Gaussian sequences Suppose that [X][1], [X][2], ... is some stationary zero mean Gaussian sequence with unit variance. Let {[k[n]]} be a certain nondecreasing sequence of positive integers, denote the [k[n]] large...
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| Veröffentlicht in: | Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 2009-01, Vol.63 (1), p.63 |
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| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The almost sure central limit theorems for certain order statistics of some stationary Gaussian sequences Suppose that [X][1], [X][2], ... is some stationary zero mean Gaussian sequence with unit variance. Let {[k[n]]} be a certain nondecreasing sequence of positive integers, denote the [k[n]] largest maximum of [X][1], ... [X[n]]. We aim at proving the almost sure central limit theorems for the suitably normalized sequence under certain additional assumptions on {[k[n]]} and the covariance function |
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| ISSN: | 0365-1029 2083-7402 |
| DOI: | 10.2478/v10062-009-0007-9 |