Invertibility of functionals of the Poisson process and applications
Probability
2026-04-02 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2307.02887,
title = {Invertibility of functionals of the Poisson process and applications},
author = {Laure Coutin and Laurent Decreusefond},
journal= {arXiv preprint arXiv:2307.02887},
year = {2026}
}