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A Note on the Extremal Index for Space-Time Processes

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

K. F. Turkman
K. F. Turkman*
Affiliation:
University of Lisbon
*
∗ Postal address: Departamento de Estatística e Investigação Operacional, Edifício C2, Cidade Universitária, Campo Grande, 1749-016 Lisboa, Portugal. Email address: kfturkman@fc.ul.pt
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Abstract

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Let {X(s, t), s = (s1, s2) ∈ ℝ2, t ∈ ℝ} be a stationary random field defined over a discrete lattice. In this paper, we consider a set of domain of attraction criteria giving the notion of extremal index for random fields. Together with the extremal-types theorem given by Leadbetter and Rootzen (1997), this will give a characterization of the limiting distribution of the maximum of such random fields.

Keywords

Extremal indexrandom field

MSC classification

Primary: 60G70: Extreme value theory; extremal processes 60G60: Random fields
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 114 - 126
Copyright
© Applied Probability Trust 2006 

References

Cliff, A. D. and Ord, J. K. (1975). Model building and the analysis of spatial pattern in human geography. J. R. Statist. Soc. B 37, 297–348.Google Scholar
Cressie, N. A. C. (1993). Statistics for Spatial Data. John Wiley, New York.Google Scholar
Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events. Springer, Berlin.CrossRefGoogle Scholar
O'Brien, G. L. (1987). Extreme values for stationary and Markov sequences. Ann. Prob. 15, 281–291.CrossRefGoogle Scholar
Leadbetter, M. R. and Rootzen, H. (1997). On extreme values in stationary random fields. Res. Rep. 507, Center for Stochastic Processes, The University of North Carolina and Chapel Hill.Google Scholar
Resnick, S. I. (1987). Extreme Values, Regular Variation, and Point Processes. Springer, New York.CrossRefGoogle Scholar