This paper is concerned with contact distribution functions of a
random closed set $\Xi=\Bigcup_{n=1}^\infty \Xi_n$ in $\mathbb{R}^d$, where the
$\Xi_n$ are assumed to be random nonempty convex bodies. These distribution
functions are defined here in terms of a distance function which is associated
with a strictly convex gauge body (structuring element) that contains the
origin in its interior. Support measures with respect to such distances will be
introduced and extended to sets in the local convex ring.These measures will
then be used in a systematic way to derive and describe some of the basic
properties of contact distribution functions. Most of the results are obtained
in a general nonstationary setting.Only the final section deals with the
stationary case.
Publié le : 2000-04-14
Classification:
Stochastic geometry,
Minkowski space,
contact distribution function,
germ-grain model,
support (curvature) measure,
marked point process,
Palm probabilities,
randommeasure,
60D05,
60G57,
52A21,
60G55,
52A22,
52A20,
53C65,
46B20
@article{1019160261,
author = {Hug, Daniel and Last, G\"unter},
title = {On support measures in Minkowski spaces and contact distributions
in stochastic geometry},
journal = {Ann. Probab.},
volume = {28},
number = {1},
year = {2000},
pages = { 796-850},
language = {en},
url = {http://dml.mathdoc.fr/item/1019160261}
}
Hug, Daniel; Last, Günter. On support measures in Minkowski spaces and contact distributions
in stochastic geometry. Ann. Probab., Tome 28 (2000) no. 1, pp. 796-850. http://gdmltest.u-ga.fr/item/1019160261/