Article Dans Une Revue The Annals of Probability Année : 2025

Invertibility of functionals of the Poisson process and applications

Résumé

Following previous investigations by Üstünel [22] about the invertibility of some transformations on the Wiener space, we find some entropic conditions under which a random change of time is invertible on the Poisson space. As a consequence, we provide a new construction of Hawkes processes. We also establish a new variational representation of the entropy.

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Dates et versions

hal-04153437 , version 1 (06-07-2023)
hal-04153437 , version 2 (26-11-2024)

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Laure Coutin, Laurent Decreusefond. Invertibility of functionals of the Poisson process and applications. The Annals of Probability, 2025, 53 (5), ⟨10.1214/24-AOP1748⟩. ⟨hal-04153437v1⟩
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