A generalization of Matérn hard-core processes with applications to max-stable processes. (December 2020)

• Record Type: Journal Article
• Authors: Dirrler, Martin; Dörr, Christopher; Schlather, Martin
• Is Part Of: Journal of applied probability. Volume 57:Number 4(2020)
• Page Start: 1298
• Page End: 1312
• Publication Date: 2020-12
• Subjects: Matérn hard-core process, -- log Gaussian Cox process, -- mixed moving maxima, -- max-domain of attraction, -- Cox extremal process; 60G55, -- 86A32, -- 60G70; 519.2
• DOI: 10.1017/jpr.2020.66
• Languages: English
• ISSNs: 0021-9002

Abstract

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.