scholarly journals Marked Gibbs Point Processes with Unbounded Interaction: An Existence Result

2020 ◽  
Vol 179 (4) ◽  
pp. 972-996
Author(s):  
Sylvie Rœlly ◽  
Alexander Zass
Keyword(s):  
Point Processes ◽  
Existence Result ◽  
Gibbs Point Processes

scholarly journals Existence of Gibbs point processes with stable infinite range interaction

2020 ◽  
Vol 57 (3) ◽  
pp. 775-791
Author(s):  
David Dereudre ◽  
Thibaut Vasseur
Keyword(s):  
Point Processes ◽  
Existence Results ◽  
Pairwise Interaction ◽  
Range Interaction ◽  
Pairwise Interactions ◽  
Gibbs Point Processes ◽  
Infinite Range Interactions ◽  
Finite Configuration ◽  
Multi Body ◽  
Infinite Range

AbstractWe provide a new proof of the existence of Gibbs point processes with infinite range interactions, based on the compactness of entropy levels. Our main existence theorem holds under two assumptions. The first one is the standard stability assumption, which means that the energy of any finite configuration is superlinear with respect to the number of points. The second assumption is the so-called intensity regularity, which controls the long range of the interaction via the intensity of the process. This assumption is new and introduced here since it is well adapted to the entropy approach. As a corollary of our main result we improve the existence results by Ruelle (1970) for pairwise interactions by relaxing the superstabilty assumption. Note that our setting is not reduced to pairwise interaction and can contain infinite-range multi-body counterparts.

scholarly journals Fast approximation of the intensity of Gibbs point processes

2012 ◽  
Vol 6 (0) ◽  
pp. 1155-1169 ◽  
Author(s):  
Adrian Baddeley ◽  
Gopalan Nair
Keyword(s):  
Point Processes ◽  
Gibbs Point Processes

Modelling Tree Roots in Mixed Forest Stands by Inhomogeneous Marked Gibbs Point Processes

2009 ◽  
Vol 51 (3) ◽  
pp. 522-539 ◽  
Author(s):  
Stefanie Eckel ◽  
Frank Fleischer ◽  
Pavel Grabarnik ◽  
Marian Kazda ◽  
Aila Särkkä ◽  
...  
Keyword(s):  
Point Processes ◽  
Mixed Forest ◽  
Forest Stands ◽  
Tree Roots ◽  
Gibbs Point Processes

scholarly journals Maximum pseudolikelihood estimator for exponential family models of marked Gibbs point processes

2008 ◽  
Vol 2 (0) ◽  
pp. 234-264 ◽  
Author(s):  
Jean-Michel Billiot ◽  
Jean-François Coeurjolly ◽  
Rémy Drouilhet
Keyword(s):  
Exponential Family ◽  
Point Processes ◽  
Gibbs Point Processes ◽  
Maximum Pseudolikelihood ◽  
Family Models
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