The paper extends to d > 1 dimensions the concept of point-stationarity, which formalizes the intuitive idea of a point process for which the behaviour relative to a given point of the process is independent of the point selected as origin. After defining point-stationarity, this concept is characterized in several ways and the characterizations then used to extend to d dimensions a particular approach to Palm theory, producing two dualities between stationary and point-stationary processes with quite different interpretations. The dualities coincide in the ergodic case.
Publié le : 1999-10-14
Classification:
coupling,
Palm theory,
point process,
random field,
stationarity,
stochastic geometry
@article{1171290400,
author = {Thorisson, Hermann},
title = {Point stationarity in d dimensions and Palm theory},
journal = {Bernoulli},
volume = {5},
number = {6},
year = {1999},
pages = { 797-831},
language = {en},
url = {http://dml.mathdoc.fr/item/1171290400}
}
Thorisson, Hermann. Point stationarity in d dimensions and Palm theory. Bernoulli, Tome 5 (1999) no. 6, pp. 797-831. http://gdmltest.u-ga.fr/item/1171290400/