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- W2900749629 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." @default.
- W2900749629 created "2018-11-29" @default.
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- W2900749629 date "2018-11-20" @default.
- W2900749629 modified "2023-09-27" @default.
- W2900749629 title "Ergodic Poisson Splittings" @default.
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