Invertibility of functionals of the Poisson process and applications

Laure Coutin, Laurent Decreusefond

Published 2023-07-06Version 1

Following previous investigations by {\"U}st{\"u}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.