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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 = (s 1, s 2) ∈ 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

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 114 - 126
Copyright
© Applied Probability Trust 2006 

References

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