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Random Marked Sets
- Part of
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- Journal:
- Advances in Applied Probability / Volume 44 / Issue 3 / September 2012
- Published online by Cambridge University Press:
- 04 January 2016, pp. 603-616
- Print publication:
- September 2012
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- Article
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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
. 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.
. 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.