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Following previous investigations by {\"U}st{\"u}nel [22] about theinvertibility of some transformations on the Wiener space, we find someentropic conditions under which a random change of time is invertible on thePoisson space. As a consequence, we provide a new construction of Hawkesprocesses. We also establish a new variational representation of the entropy.

Invertibility of functionals of the Poisson process and applications