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Asymptotic distribution of the maximum of n independent stochastic processes

Part of: Nonparametric inference Limit theorems

Published online by Cambridge University Press:  14 July 2016

A. A. Balkema ,
L. De Haan  and
R. L. Karandikar
A. A. Balkema*
Affiliation:
University of Amsterdam
L. De Haan*
Affiliation:
Erasmus University, Rotterdam
R. L. Karandikar*
Affiliation:
Indian Statistical Institute, New Delhi
*
∗ Postal address: Mathematical Institute, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands.
∗∗ Postal address: Econometric Institute, Erasmus University, Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands.
∗∗∗ Postal address: Indian Statistical Institute, 7 S. J. S. Sansanwal Marg, New Delhi 110 016, India.
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Abstract

Limits in distribution of maxima of independent stochastic processes are characterized in terms of spectral functions acting on a Poisson point process.

Keywords

EXTREME VALUESLIMIT LAWS

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 62G30: Order statistics; empirical distribution functions
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 1 , March 1993 , pp. 66 - 81
Copyright
Copyright © Applied Probability Trust 1993 

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References

Balkema, A. A. and Resnick, S. I. (1977) Max-infinite divisibility. J. Appl. Prob. 14, 309–319.Google Scholar
Brozius, H. and De Haan, L. (1987) On limiting laws for the convex hull of a sample. J. Appl. Prob. 24, 852–862.Google Scholar
Gerritse, G. (1986) Supremum self-decomposable random vectors. Prob. Theory Rel. Fields 72, 17–33.Google Scholar
Giné, E., Hahn, M. G. and Vatan, P. (1990) Max infinitely divisible and max stable sample continuous processes. Prob. Theory Rel. Fields 82, 139–165.Google Scholar
De Haan, L. (1984), A spectral representation for max-stable processes. Ann. Prob. 12, 1194–1204.Google Scholar
De Haan, L. (1990) Fighting the arch-enemy with mathematics. Statist. Neerlandica 44, 45–68.Google Scholar
Mejzler, D. (1956) On the problem of the limit distributions for the maximal term of a variational series. Lvov Politechn Inst. Naucn. Zap. Ser. Fiz.-Mat. 38, 90–109 (Russian).Google Scholar
O'Brien, G. L., Torfs, P. and Vervaat, W. (1990) Selfsimilar stationary extremal processes. Prob. Theory Rel. Fields. 87, 97–119.Google Scholar
Pancheva, E. I. (1990) Self-decomposable distributions for maxima of independent random vectors. Prob. Theory Rel. Fields 84, 267–278.CrossRefGoogle Scholar
Rényi, A. (1967) Remarks on the Poisson process. Studia Sci. Math. Hung. 2, 119–123.Google Scholar
Resnick, S. I. (1987) Extreme Values, Regular Variation and Point Processes. Springer, New York.Google Scholar
Rockafellar, R. T. (1970) Convex Analysis. Princeton University Press.Google Scholar
Royden, H. L. (1968) Real Analysis. Collier MacMillan London.Google Scholar
Vatan, P. (1985) Max-infinite divisibility and max-stability in infinite dimensions. Lecture Notes in Mathematics, 1153, 400–425. Springer-Verlag, New York.Google Scholar