We introduce and study invariant (weighted) transport-kernels balancing stationary random measures on a locally compact Abelian group. The first main result is an associated fundamental invariance property of Palm measures, derived from a generalization of Neveu’s exchange formula. The second main result is a simple sufficient and necessary criterion for the existence of balancing invariant transport-kernels. We then introduce (in a nonstationary setting) the concept of mass-stationarity with respect to a random measure, formalizing the intuitive idea that the origin is a typical location in the mass. The third main result of the paper is that a measure is a Palm measure if and only if it is mass-stationary.
Publié le : 2009-03-15
Classification:
Stationary random measure,
invariant transport-kernel,
allocation rule,
Palm measure,
Abelian group,
mass-stationarity,
60G57,
60G55,
60G60
@article{1241099929,
author = {Last, G\"unter and Thorisson, Hermann},
title = {Invariant transports of stationary random measures and mass-stationarity},
journal = {Ann. Probab.},
volume = {37},
number = {1},
year = {2009},
pages = { 790-813},
language = {en},
url = {http://dml.mathdoc.fr/item/1241099929}
}
Last, Günter; Thorisson, Hermann. Invariant transports of stationary random measures and mass-stationarity. Ann. Probab., Tome 37 (2009) no. 1, pp. 790-813. http://gdmltest.u-ga.fr/item/1241099929/