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arXiv · 2307.02887

Invertibility of functionals of the Poisson process and applications

Laure Coutin·Laurent Decreusefond
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Abstract

Following previous investigations by {Ü}st{ü}nel [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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Laure Coutin, Laurent Decreusefond. 2024-11-28. Invertibility of functionals of the Poisson process and applications. https://doi.org/10.1214/24-aop1748

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