ERGODIC POISSON SPLITTINGS

• 成果类型: Article
• 署名作者: Janvresse, Elise; Roy, Emmanuel; de la Rue, Thierry
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Picardie Jules Verne (UPJV); Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); Universite de Rouen Normandie
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1390
• 发表日期: 2020
• 页码: 1266-1285
• 关键词: quasi-factors

摘要

In this paper, we study splittings of a Poisson point process which are equivariant under a conservative transformation. We show that, if the Cartesian powers of this transformation are all ergodic, the only ergodic splitting is the obvious one, that is, a collection of independent Poisson processes. We apply this result to the case of a marked Poisson process: under the same hypothesis, the marks are necessarily independent of the point process and i.i.d. Under additional assumptions on the transformation, a further application is derived, giving a full description of the structure of a random measure invariant under the action of the transformation.