Invariant transports of stationary random measures and mass-stationarity

Details Invariant transports of stationary random measures and mass-stationarity Invariant transports of stationary random measures and mass-stationarity

2009-06-11

arxiv.org/abs/0906.2062v1

Annals of Probability 2009, Vol. 37, No. 2, 790-813

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AOP420 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

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.

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