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Preprints, Working Papers, ... Year : 2023

Invertibility of functionals of the Poisson process and applications

Abstract

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 and versions

hal-04153437 , version 1 (06-07-2023)

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Laure Coutin, Laurent Decreusefond. Invertibility of functionals of the Poisson process and applications. 2023. ⟨hal-04153437⟩
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