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AN ALMOST SURE LIMIT THEOREM FOR THE MAXIMA OF MULTIVARIATE STATIONARY GAUSSIAN SEQUENCES

Part of: Limit theorems

Published online by Cambridge University Press:  01 June 2009

ZHICHENG CHEN ,
ZUOXIANG PENG  and
HONGYUN ZHANG
ZHICHENG CHEN
Affiliation:
Department of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, PR China (email: [email protected])
ZUOXIANG PENG*
Affiliation:
School of Mathematics and Statistics, Southwest University, Chongqing 400715, PR China (email: [email protected])
HONGYUN ZHANG
Affiliation:
Department of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, PR China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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An almost sure limit theorem for the maxima of multivariate stationary Gaussian sequences is proved under some mild conditions.

Keywords

almost sure central limit theoremmultivariate stationary Gaussian sequences

MSC classification

Secondary: 60F15: Strong theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 3 , June 2009 , pp. 315 - 321
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This work was partially supported by the National Natural Science Foundation of China (grant no. 70371061).

References

[1]Amram, F., ‘Multivariate extreme value distributions for stationary Gaussian sequences’, J. Multivariate Anal. 16 (1985), 237–240.CrossRefGoogle Scholar
[2]Berkes, I. and Csáki, E., ‘A universal result in almost sure central limit theory’, Stochastic Process. Appl. 94 (2001), 105–134.CrossRefGoogle Scholar
[3]Berkes, I., Csáki, E. and Horváth, L., ‘Almost sure central limit theorems under minimal conditions’, Statist. Probab. Lett. 37 (1998), 67–76.CrossRefGoogle Scholar
[4]Brosamler, G., ‘An almost everywhere central limit theorem’, Math. Proc. Cambridge Philos. Soc. 104 (1988), 561–574.CrossRefGoogle Scholar
[5]Chen, S. and Lin, Z., ‘Almost sure max-limits for nonstationary Gaussian sequence’, Statist. Probab. Lett. 76 (2006), 1175–1184.CrossRefGoogle Scholar
[6]Cheng, S., Peng, L. and Qi, Y., ‘Almost sure convergence in extreme value theory’, Math. Nachr. 190 (1998), 43–50.CrossRefGoogle Scholar
[7]Csáki, E. and Gonchigdanzan, K., ‘Almost sure limit theorem for the maximum of stationary Gaussian sequences’, Statist. Probab. Lett. 58 (2002), 195–203.CrossRefGoogle Scholar
[8]Fahrner, I. and Stadtmüller, U., ‘On almost sure max-limit theorems’, Statist. Probab. Lett. 37 (1998), 229–236.CrossRefGoogle Scholar
[9]Fazekas, I. and Chuprunov, A., ‘An almost sure functional limit theorem for the domain of geometric partial attraction of semistable laws’, J. Theoret. Probab. 20 (2007), 339–353.CrossRefGoogle Scholar
[10]Hüsler, J., ‘Multivariate extreme value in stationary random sequences’, Stochastic Process. Appl. 35 (1990), 109–119.CrossRefGoogle Scholar
[11]Lacey, M. and Philipp, W., ‘A note on the almost sure central limit theorem’, Statist. Probab. Lett. 9 (1990), 201–205.CrossRefGoogle Scholar
[12]Leadbetter, M. R., Lindgren, G. and Rootzén, H., Extremes and Related Properties of Random Sequences and Processes (Springer, New York, 1983).CrossRefGoogle Scholar
[13]Resnick, S. I., Extreme Values, Regular Variation and Point Processes (Springer, New York, 1987).CrossRefGoogle Scholar
[14]Schatte, P., ‘On strong versions of the central limit theorem’, Math. Nachr. 137 (1988), 249–256.CrossRefGoogle Scholar