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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