Random Marked Sets
Probability
2012-01-25 v2
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.
Cite
@article{arxiv.0903.2388,
title = {Random Marked Sets},
author = {Felix Ballani and Zakhar Kabluchko and Martin Schlather},
journal= {arXiv preprint arXiv:0903.2388},
year = {2012}
}