Open Access
March 2009 Invariant transports of stationary random measures and mass-stationarity
Günter Last, Hermann Thorisson
Ann. Probab. 37(2): 790-813 (March 2009). DOI: 10.1214/08-AOP420


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.


Download Citation

Günter Last. Hermann Thorisson. "Invariant transports of stationary random measures and mass-stationarity." Ann. Probab. 37 (2) 790 - 813, March 2009.


Published: March 2009
First available in Project Euclid: 30 April 2009

zbMATH: 1176.60036
MathSciNet: MR2510024
Digital Object Identifier: 10.1214/08-AOP420

Primary: 60G55 , 60G57
Secondary: 60G60

Keywords: Abelian group , allocation rule , invariant transport-kernel , mass-stationarity , Palm measure , Stationary random measure

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 2 • March 2009
Back to Top