# The almost sure central limit theorems for certain order statistics of some stationary Gaussian sequences

Annales UMCS, Mathematica (2009)

- Volume: 63, Issue: 1, page 63-81
- ISSN: 2083-7402

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topMarcin Dudziński. "The almost sure central limit theorems for certain order statistics of some stationary Gaussian sequences." Annales UMCS, Mathematica 63.1 (2009): 63-81. <http://eudml.org/doc/268257>.

@article{MarcinDudziński2009,

abstract = {Suppose that X1, X2, … is some stationary zero mean Gaussian sequence with unit variance. Let \{kn\} be a certain nondecreasing sequence of positive integers, [...] denote the kn largest maximum of X1, … Xn. We aim at proving the almost sure central limit theorems for the suitably normalized sequence [...] under certain additional assumptions on \{kn\} and the covariance function [...]},

author = {Marcin Dudziński},

journal = {Annales UMCS, Mathematica},

keywords = {Almost sure central limit theorem; knth largest maxima; stationary Gaussian sequences; Normal Comparison Lemma; almost sure central limit theorem; th largest maxima; normal comparison Lemma},

language = {eng},

number = {1},

pages = {63-81},

title = {The almost sure central limit theorems for certain order statistics of some stationary Gaussian sequences},

url = {http://eudml.org/doc/268257},

volume = {63},

year = {2009},

}

TY - JOUR

AU - Marcin Dudziński

TI - The almost sure central limit theorems for certain order statistics of some stationary Gaussian sequences

JO - Annales UMCS, Mathematica

PY - 2009

VL - 63

IS - 1

SP - 63

EP - 81

AB - Suppose that X1, X2, … is some stationary zero mean Gaussian sequence with unit variance. Let {kn} be a certain nondecreasing sequence of positive integers, [...] denote the kn largest maximum of X1, … Xn. We aim at proving the almost sure central limit theorems for the suitably normalized sequence [...] under certain additional assumptions on {kn} and the covariance function [...]

LA - eng

KW - Almost sure central limit theorem; knth largest maxima; stationary Gaussian sequences; Normal Comparison Lemma; almost sure central limit theorem; th largest maxima; normal comparison Lemma

UR - http://eudml.org/doc/268257

ER -

## References

top- Csaki, E., Gonchigdanzan, K., Almost sure limit theorem for the maximum of stationary Gaussian sequences, Statist. Probab. Lett. 58 (2002), 195-203. Zbl1014.60031
- Dudziński, M., An almost sure maximum limit theorem for certain class of dependent stationary Gaussian sequences, Demonstratio Math. 35 (4) (2002), 879-890. Zbl1011.60010
- Leadbetter, M. R., Lindgren, G. and Rootzen, H., Extremes and Related Properties of Random Sequences and Processes, Springer-Verlag, New York, Heidelberg, Berlin, 1983. Zbl0518.60021
- Stadtmueller, U., Almost sure versions of distributional limit theorems for certain order statistics, Statist. Probab. Lett. 58 (2002), 413-426. Zbl1033.60042

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