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A generalization of Matérn hard-core processes with applications to max-stable processes

Part of: Stochastic processes Geophysics (general) Geophysics

Published online by Cambridge University Press:  23 November 2020

Martin Dirrler ,
Christopher Dörr  and
Martin Schlather
Martin Dirrler*
Affiliation:
Landesbank Baden-Württemberg
Martin Schlather*
Affiliation:
University of Mannheim
*
*Postal address: Landesbank Baden-Württemberg, P.O. Box 106049, 70049, Stuttgart, Germany.
*Postal address: Landesbank Baden-Württemberg, P.O. Box 106049, 70049, Stuttgart, Germany.
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Abstract

Matérn hard-core processes are classical examples for point processes obtained by dependent thinning of (marked) Poisson point processes. We present a generalization of the Matérn models which encompasses recent extensions of the original Matérn hard-core processes. It generalizes the underlying point process, the thinning rule, and the marks attached to the original process. Based on our model, we introduce processes with a clear interpretation in the context of max-stable processes. In particular, we prove that one of these processes lies in the max-domain of attraction of a mixed moving maxima process.

Keywords

Matérn hard-core processlog Gaussian Cox processmixed moving maximamax-domain of attractionCox extremal process

MSC classification

Primary: 60G55: Point processes
Secondary: 86A32: Geostatistics 60G70: Extreme value theory; extremal processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 4 , December 2020 , pp. 1298 - 1312
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Copyright
© Applied Probability Trust 2020

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