Point shift characterization of Palm measures on Abelian groups
Matthias Heveling, Karlsruhe University
Gunter Last, Karlsruhe University
Abstract
Our first aim in this paper is to characterize Palm measures of
stationary point processes through point stationarity.
This generalizes earlier results from the Euclidean case
to the case of an Abelian group.
While a stationary point process looks statistically the
same from each site, a point stationary point process
looks statistically the same from each of its points.
Even in the Euclidean case our proof will simplify some of
the earlier arguments. A new technical result of some independent interest is the
existence of a complete countable family of matchings.
Using a change of measure we will generalize our results to discrete random
measures. In the Euclidean case we will finally treat general random measures
by means of a suitable approximation.
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