A spatial Markov property for nearest-neighbour Markov point processes

1990 ◽  
Vol 27 (04) ◽  
pp. 767-778 ◽  
Author(s):  
W. S. Kendall
Keyword(s):  
Point Processes ◽  
Markov Property ◽  
Nearest Neighbour ◽  
Markov Point Processes

Nearest-neighbour Markov point processes were introduced by Baddeley and Møller (1989) as generalizations of the Markov point processes of Ripley and Kelly. This note formulates and discusses a spatial Markov property for these point processes.

A spatial Markov property for nearest-neighbour Markov point processes

1990 ◽  
Vol 27 (4) ◽  
pp. 767-778 ◽  
Author(s):  
W. S. Kendall
Keyword(s):  
Point Processes ◽  
Markov Property ◽  
Nearest Neighbour ◽  
Markov Point Processes

Nearest-neighbour Markov point processes were introduced by Baddeley and Møller (1989) as generalizations of the Markov point processes of Ripley and Kelly. This note formulates and discusses a spatial Markov property for these point processes.

scholarly journals Nearest-neighbour Markov point processes on graphs with Euclidean edges

2018 ◽  
Vol 50 (4) ◽  
pp. 1275-1293 ◽  
Author(s):  
M. N. M. van Lieshout
Keyword(s):  
Real Line ◽  
Point Processes ◽  
Local Geometry ◽  
Renewal Processes ◽  
Nearest Neighbour ◽  
The Real ◽  
Consistency Conditions ◽  
Linear Networks ◽  
Markov Point Processes ◽  
Neighbour Point

Abstract We define nearest-neighbour point processes on graphs with Euclidean edges and linear networks. They can be seen as analogues of renewal processes on the real line. We show that the Delaunay neighbourhood relation on a tree satisfies the Baddeley‒Møller consistency conditions and provide a characterisation of Markov functions with respect to this relation. We show that a modified relation defined in terms of the local geometry of the graph satisfies the consistency conditions for all graphs with Euclidean edges that do not contain triangles.

Nearest-Neighbour Markov Point Processes and Random Sets

1989 ◽  
Vol 57 (2) ◽  
pp. 89 ◽  
Author(s):  
Adrian Baddeley ◽  
Jesper Møller ◽  
Jesper Moller
Keyword(s):  
Point Processes ◽  
Random Sets ◽  
Nearest Neighbour ◽  
Markov Point Processes

scholarly journals Markov properties of cluster processes

1996 ◽  
Vol 28 (2) ◽  
pp. 346-355 ◽  
Author(s):  
A. J. Baddeley ◽  
M. N. M. Van Lieshout ◽  
J. Møller
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Markov Property ◽  
Nearest Neighbour ◽  
Finite Range ◽  
Cluster Process ◽  
Cluster Point Process ◽  
Poisson Cluster ◽  
Markov Properties ◽  
Uniformly Bounded

We show that a Poisson cluster point process is a nearest-neighbour Markov point process [2] if the clusters have uniformly bounded diameter. It is typically not a finite-range Markov point process in the sense of Ripley and Kelly [12]. Furthermore, when the parent Poisson process is replaced by a Markov or nearest-neighbour Markov point process, the resulting cluster process is also nearest-neighbour Markov, provided all clusters are non-empty. In particular, the nearest-neighbour Markov property is preserved when points of the process are independently randomly translated, but not when they are randomly thinned.

Markov point processes

1978 ◽  
Vol 10 (2) ◽  
pp. 262-263
Author(s):  
Erhan Çinlar
Keyword(s):  
Point Processes ◽  
Markov Point Processes

Transformations of Markov point processes

1998 ◽  
Vol 30 (2) ◽  
pp. 281-281
Author(s):  
Eva B. Vedel Jensen ◽  
Linda Stougaard Nielsen
Keyword(s):  
Point Processes ◽  
Markov Point Processes

Markov property of point processes

1987 ◽  
Vol 76 (1) ◽  
pp. 71-80 ◽  
Author(s):  
Hans G. Kellerer
Keyword(s):  
Point Processes ◽  
Markov Property
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