Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T14:45:22.843Z Has data issue: false hasContentIssue false
  • English
  • Français

Extreme values of non-stationary random sequences

Published online by Cambridge University Press:  24 August 2016

Jürg Hüsler
Jürg Hüsler*
Affiliation:
University of Bern
*
∗Postal address: Universität Bern, Institut für Mathematische Statistik und Versicherungslehre, Sidlerstrasse 5, CH-3012 Bern, Switzerland.
Get access Rights & Permissions [Opens in a new window]

Abstract

We extend some results of the extreme-value theory of stationary random sequences to non-stationary random sequences. The extremal index, defined in the stationary case, plays a similar role in the extended case. The details show that this index describes not only the behaviour of exceedances above a high level but also above a non-constant high boundary.

Keywords

EXTREMAL INDEXEXCEEDANCE
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 937 - 950
Copyright
Copyright © Applied Probability Trust 1986 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Part of this research was done while the author was at the Center for Stochastic Processes at Chapel Hill. The author wishes to express his gratitude for the financial support and the hospitality.

References

[1] Chernick, M. R. (1981) A limit theorem for the maximum of autoregressive processes with uniform marginal distribution. Ann. Prob. 9, 146–149.CrossRefGoogle Scholar
[2] Denzel, G. E. and O'Brien, G. L. (1975) Limit theorems for extreme values of chain-dependent processes. Ann. Prob. 3, 773–779.CrossRefGoogle Scholar
[3] Galambos, J. (1978) The Asymptotic Theory of Extreme Order Statistics. Wiley, New York.Google Scholar
[4] Hüsler, J. (1983) Asymptotic approximation of crossing probabilities of random sequences. Z. Wahrscheinlichkeitsth. 63, 257–270.Google Scholar
[5] Leadbetter, M. R. (1974) On extreme values in stationary sequences. Z. Wahrscheinlichkeitsth. 28, 289–303.CrossRefGoogle Scholar
[6] Leadbetter, M. R. (1983) Extremes and local dependence in stationary sequences. Z. Wahrscheinlichkeitsth. 65, 291–306.Google Scholar
[7] Leadbetter, M. R., Lindgren, G. and Rootzen, H. (1983) Extremes and Related Properties of Random Sequences and Processes. Springer-Verlag, New York.Google Scholar
[8] Rootzen, H. (1978) Extremes of moving averages of stable processes. Ann. Prob. 6, 847–869.Google Scholar