Ergodic Poisson splittings
| Autor: | Emmanuel Roy, Thierry de la Rue, Elise Janvresse |
|---|---|
| Přispěvatelé: | Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 (LAMFA), Université de Picardie Jules Verne (UPJV)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), Laboratoire de Mathématiques Raphaël Salem (LMRS), Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), GdR GeoSto |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Poisson suspension Pure mathematics splitting [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] Dynamical Systems (math.DS) Poisson distribution 01 natural sciences Point process 010104 statistics & probability symbols.namesake Poisson point process FOS: Mathematics Ergodic theory 37A50 0101 mathematics Mathematics - Dynamical Systems Mathematics Probability (math.PR) 010102 general mathematics thinning 37A40 joinings Invariant (physics) [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Random measure Transformation (function) symbols Equivariant map 60G57 60G55 Statistics Probability and Uncertainty Mathematics - Probability random measure |
| Zdroj: | Ann. Probab. 48, no. 3 (2020), 1266-1285 Annals of Probability Annals of Probability, Institute of Mathematical Statistics, 2020, 48 (3), pp.1266-1285. ⟨10.1214/19-AOP1390⟩ |
| ISSN: | 0091-1798 2168-894X |
| DOI: | 10.1214/19-AOP1390⟩ |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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