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May 2020 Ergodic Poisson splittings
Élise Janvresse, Emmanuel Roy, Thierry de la Rue
Ann. Probab. 48(3): 1266-1285 (May 2020). DOI: 10.1214/19-AOP1390

Abstract

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.

Citation

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Élise Janvresse. Emmanuel Roy. Thierry de la Rue. "Ergodic Poisson splittings." Ann. Probab. 48 (3) 1266 - 1285, May 2020. https://doi.org/10.1214/19-AOP1390

Information

Received: 1 November 2018; Published: May 2020
First available in Project Euclid: 17 June 2020

zbMATH: 07226360
MathSciNet: MR4112714
Digital Object Identifier: 10.1214/19-AOP1390

Subjects:
Primary: 37A50, 60G55, 60G57
Secondary: 37A40

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 3 • May 2020
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