Advances in Applied Probability

Random marked sets

F. Ballani, Z. Kabluchko, and M. Schlather

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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 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.

Article information

Adv. in Appl. Probab., Volume 44, Number 3 (2012), 603-616.

First available in Project Euclid: 6 September 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G60: Random fields 60G55: Point processes
Secondary: 60G15: Gaussian processes 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Random field random set marked point process mark correlation function mark covariance function


Ballani, F.; Kabluchko, Z.; Schlather, M. Random marked sets. Adv. in Appl. Probab. 44 (2012), no. 3, 603--616. doi:10.1239/aap/1346955256.

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