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Limit laws for the maxima of a class of quasi-stationary sequences

Published online by Cambridge University Press:  14 July 2016

K. F. Turkman  and
A. M. Walker
K. F. Turkman
Affiliation:
University of Sheffield
A. M. Walker*
Affiliation:
University of Sheffield
*
∗∗ Postal address: Department of Probability and Statistics, The University, Sheffield S3 7RH, U.K.
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Abstract

A class of quasi-stationary sequences of random variables is introduced. After giving the definition, it is shown that the limiting distributions of the maxima of such sequences, when suitably normalized, converge to one of the three extreme-value distributions.

Keywords

EXTREME-VALUE DISTRIBUTIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 4 , December 1983 , pp. 814 - 821
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

∗)

Present address: Faculdade de Ciencias da Universidade de Lisboa, Departamento de Estatistica, Investigaçá o Operacional e Computaçá o, 58 Rua da Escola Politécnica, 1294 Lisboa Codex, Portugal.

References

Chung, K. L. (1974) A Course in Probability Theory, 2nd edn. Academic Press, New York.Google Scholar
Leadbetter, M. R. (1974) On extreme values in stationary sequences. Z. Wahrscheinlichkeitsth. 28, 289–303.CrossRefGoogle Scholar
Resnick, S. I. (1971) Tail equivalence and applications. J. Appl. Prob. 8, 136–156.Google Scholar
Resnick, S. I. and Neuts, M. F. (1970) Limit laws for maxima of a sequence of random variables defined on a Markov chain. Adv. Appl. Prob. 2, 323–343.Google Scholar
Tiago De Oliveira, J. (1976) Asymptotic behaviour of maxima with periodic disturbances. Ann. Inst. Statist. Math. 28, 19–23.CrossRefGoogle Scholar
Turkman, K. F. (1980) Limiting Distributions of Maxima of Certain Types of Non-Stationary Stochastic Processes. , University of Sheffield.Google Scholar