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Poisson suspensions and SuShis. (Suspensions de Poisson et SuShis.) (English. French summary) Zbl 1382.37006
A theorem due to C. Foiaş and S. Stratila [C. R. Acad. Sci., Paris, Sér. A 267, 166–168 (1968; Zbl 0218.60040)] states that some spectral measures of some ergodic stationary processes force the process to be Gaussian. In this paper, the authors obtain a Poisson counterpart of the above mentioned result, by proving that some ergodic infinite measure-preserving transformations of an ergodic invariant point process with moments of all orders force the process to be a superposition of shifted Poisson point processes.

MSC:
37A50 Dynamical systems and their relations with probability theory and stochastic processes
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
37A40 Nonsingular (and infinite-measure preserving) transformations
37A05 Dynamical aspects of measure-preserving transformations
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