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Space‒time max-stable models with spectral separability

Part of: Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  25 July 2016

Paul Embrechts ,
Erwan Koch  and
Christian Robert
Paul Embrechts*
Affiliation:
ETH Zürich
Erwan Koch*
Affiliation:
ETH Zürich
Christian Robert*
Affiliation:
Université Lyon 1
*
Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland. Email address: paul.embrechts@math.ethz.ch
Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland. Email address: erwan.koch@math.ethz.ch
ISFA, Université Lyon 1, 50 Avenue Tony Garnier, 69366 Lyon Cedex 07, France. Email address: christian.robert@univ-lyon1.fr
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Abstract

Natural disasters may have considerable impact on society as well as on the (re-)insurance industry. Max-stable processes are ideally suited for the modelling of the spatial extent of such extreme events, but it is often assumed that there is no temporal dependence. Only a few papers have introduced spatiotemporal max-stable models, extending the Smith, Schlather and Brown‒Resnick spatial processes. These models suffer from two major drawbacks: time plays a similar role to space and the temporal dynamics are not explicit. In order to overcome these defects, we introduce spatiotemporal max-stable models where we partly decouple the influence of time and space in their spectral representations. We introduce both continuous- and discrete-time versions. We then consider particular Markovian cases with a max-autoregressive representation and discuss their properties. Finally, we briefly propose an inference methodology which is tested through a simulation study.

Keywords

Extreme value theoryspatiotemporal max-stable processspectral separabilitytemporal dependence

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60G60: Random fields 62M30: Spatial processes
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue A: Probability, Analysis and Number Theory , July 2016 , pp. 77 - 97
Copyright
Copyright © Applied Probability Trust 2016 

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