Prediction of catastrophes in space over time
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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.
KeywordsGaussian random fields Spatio-temporal models Upcrossings Palm distribution Alarms Optimal prediction Catastrophes Likelihood ratio Reliability
AMS 2000 Subject ClassificationsPrimary—60G10, 60G25, 60G70
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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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