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Extremes

, Volume 21, Issue 4, pp 601–628 | Cite as

Prediction of catastrophes in space over time

  • Anastassia Baxevani
  • Richard Wilson
Article
  • 48 Downloads

Abstract

Predicting rare events, such as high level up-crossings, for spatio-temporal processes plays an important role in the analysis of the occurrence and impact of potential catastrophes in, for example, environmental settings. Designing a system which predicts these events with high probability, but with few false alarms, is clearly desirable. In this paper an optimal alarm system in space over time is introduced and studied in detail. These results generalize those obtained by de Maré (Ann. Probab. 8, 841–850, 1980) and Lindgren (Ann. Probab. 8, 775–792, 1980, Ann. Probab. 13, 804–824, 1985) for stationary stochastic processes evolving in continuous time and are applied here to stationary Gaussian random fields.

Keywords

Gaussian random fields Spatio-temporal models Upcrossings Palm distribution Alarms Optimal prediction Catastrophes Likelihood ratio Reliability 

AMS 2000 Subject Classifications

Primary—60G10, 60G25, 60G70 

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Notes

Acknowledgements

The first author would like to thank Dr Manuel Scotto for an invitation to the Department of Mathematics at the University of Aveiro, Portugal that lead to the idea of the present paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CyprusNicosiaCyprus
  2. 2.School of Mathematics and PhysicsThe University of QueenslandSt LuciaAustralia

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