scholarly journals Analytic Properties and Covariance Functions for a New Class of Generalized Gibbs Random Fields

2007 ◽  
Vol 53 (12) ◽  
pp. 4667-4679 ◽  
Author(s):  
Dionissios T. Hristopulos ◽  
Samuel N. Elogne
Keyword(s):  
Random Fields ◽  
New Class ◽  
Covariance Functions ◽  
Gibbs Random Fields

Matérn Cross-Covariance Functions for Multivariate Random Fields

2010 ◽  
Vol 105 (491) ◽  
pp. 1167-1177 ◽  
Author(s):  
Tilmann Gneiting ◽  
William Kleiber ◽  
Martin Schlather
Keyword(s):  
Random Fields ◽  
Covariance Functions ◽  
Cross Covariance

scholarly journals Random Marked Sets

2012 ◽  
Vol 44 (3) ◽  
pp. 603-616 ◽  
Author(s):  
F. Ballani ◽  
Z. Kabluchko ◽  
M. Schlather
Keyword(s):  
Random Fields ◽  
Covariance Function ◽  
Point Processes ◽  
Marked Point ◽  
Positive Definiteness ◽  
Gaussian Random Fields ◽  
Marked Point Processes ◽  
Random Set ◽  
Geostatistical Methods ◽  
New Class

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.

Sign in / Sign up

Export Citation Format

Share Document