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Geostatistics of dependent and asymptotically independent extremes. (English) Zbl 1321.86016

Summary: Spatial modeling of rare events has obvious applications in the environmental sciences and is crucial when assessing the effects of catastrophic events (such as heatwaves or widespread flooding) on food security and on the sustainability of societal infrastructure. Although classical geostatistics is largely based on Gaussian processes and distributions, these are not appropriate for extremes, for which maxstable and related processes provide more suitable models. This paper provides a brief overview of current work on the statistics of spatial extremes, with an emphasis on the consequences of the assumption of max-stability. Applications to winter minimum temperatures and daily rainfall are described.

MSC:

86A32 Geostatistics
62G32 Statistics of extreme values; tail inference
62M30 Inference from spatial processes
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