INVARIANT TRANSPORTS OF STATIONARY RANDOM MEASURES AND MASS-STATIONARITY

• 成果类型: Article
• 署名作者: Last, Guenter; Thorisson, Hermann
• 署名单位: Helmholtz Association; Karlsruhe Institute of Technology; University of Iceland
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP420
• 发表日期: 2009
• 页码: 790-813
• 关键词: point-processes; palm measures; random shifts; random-fields; head

摘要

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.