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arXiv · 0903.2388

Random Marked Sets

Felix Ballani·Zakhar Kabluchko·Martin Schlather
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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 R^d. Unlike for random fields, the mark covariance function of a marked random 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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Felix Ballani, Zakhar Kabluchko, Martin Schlather. 2009-03-13. Random Marked Sets. https://arxiv.org/abs/0903.2388

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