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September 2012 Random marked sets
F. Ballani, Z. Kabluchko, M. Schlather
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Adv. in Appl. Probab. 44(3): 603-616 (September 2012). DOI: 10.1239/aap/1346955256

Abstract

We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in Rd. Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite. This implies that in many situations the use of simple geostatistical methods appears to be questionable. Surprisingly, for a special class of processes based on Gaussian random fields, we do have positive definiteness for the corresponding mark covariance function and mark correlation function.

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F. Ballani. Z. Kabluchko. M. Schlather. "Random marked sets." Adv. in Appl. Probab. 44 (3) 603 - 616, September 2012. https://doi.org/10.1239/aap/1346955256

Information

Published: September 2012
First available in Project Euclid: 6 September 2012

zbMATH: 1266.60091
MathSciNet: MR3024601
Digital Object Identifier: 10.1239/aap/1346955256

Subjects:
Primary: 60G55, 60G60
Secondary: 60D05, 60G15

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 3 • September 2012
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