Invariant transports of stationary random measures and mass-stationarity

Last, Günter
Thorisson, Hermann

facul_07; 23

Abstract:
We introduce and discuss balancing invariant transports of stationary random measures
on a Polish 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 transports.
We then introduce (in a non-stationary 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.

Primary MSC: 60G57 Random measures, 60G55 Point processes
Secondary MSC: 60G60 Random fields
Keywords: stationary random measure, invariant transport, transport-map, Palm measure, Abelian group, mass-stationarity