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

Published online by Cambridge University Press:  23 November 2020

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.

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.

Type
Research Papers
Copyright
© Applied Probability Trust 2020

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