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On generalized max-linear models in max-stable random fields

Part of: Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  15 September 2017

Michael Falk  and
Maximilian Zott
Michael Falk*
Affiliation:
University of Würzburg
Maximilian Zott*
Affiliation:
University of Würzburg
*
* Postal address: Institute of Mathematics, University of Würzburg, Emil-Fischer-Str. 30, 97074 Würzburg, Germany.
* Postal address: Institute of Mathematics, University of Würzburg, Emil-Fischer-Str. 30, 97074 Würzburg, Germany.
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Abstract

In practice, it is not possible to observe a whole max-stable random field. Therefore, we propose a method to reconstruct a max-stable random field in C([0, 1]k) by interpolating its realizations at finitely many points. The resulting interpolating process is again a max-stable random field. This approach uses a generalized max-linear model. Promising results have been established in the k = 1 case of Falk et al. (2015). However, the extension to higher dimensions is not straightforward since we lose the natural order of the index space.

Keywords

Multivariate extreme value distributionmax-stable random fieldD-normmax-linear modelstochastic interpolation

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 62M40: Random fields; image analysis
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 3 , September 2017 , pp. 797 - 810
Copyright
Copyright © Applied Probability Trust 2017 

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