This paper deals with a weak convergence of maximum vectors built on the base of stationary and normal sequences of relatively strongly dependent random vectors. The discussion concentrates on the normality of limits and extends some results of McCormick and Mittal [4] to the multivariate case.
@article{bwmeta1.element.bwnjournal-article-zmv25i3p375bwm,
author = {Mateusz Wi\'sniewski},
title = {Extremes in multivariate stationary normal sequences},
journal = {Applicationes Mathematicae},
volume = {25},
year = {1998},
pages = {375-379},
zbl = {0998.60052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv25i3p375bwm}
}
Wiśniewski, Mateusz. Extremes in multivariate stationary normal sequences. Applicationes Mathematicae, Tome 25 (1998) pp. 375-379. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv25i3p375bwm/
[000] [1] S. M. Berman, Limit theorems for the maximum term in stationary sequences, Ann. Math. Statist. 35 (1964), 502-516. | Zbl 0122.13503
[001] [2] J. Galambos, The Asymptotic Theory of Extreme Order Statistics, Wiley, New York, 1978. | Zbl 0381.62039
[002] [3] M. R. Leadbetter, G. Lindgren and H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer, New York, 1983. | Zbl 0518.60021
[003] [4] W. P. McCormick and Y. Mittal, On weak convergence of the maximum, Techn. Report No 81, Dept. of Statist. Stanford Univ., 1976.
[004] [5] Y. Mittal and D. Ylvisaker, Limit distributions for the maxima of stationary Gaussian processes, Stochastic Process. Appl. 3 (1975), 1-18.
[005] [6] M. Wiśniewski, Extreme order statistics in an equally correlated Gaussian array, Appl. Math. (Warsaw) 22 (1994), 193-200. | Zbl 0809.62012