{
  "id": "2307.02887",
  "version": "v1",
  "published": "2023-07-06T09:43:42.000Z",
  "updated": "2023-07-06T09:43:42.000Z",
  "title": "Invertibility of functionals of the Poisson process and applications",
  "authors": [
    "Laure Coutin",
    "Laurent Decreusefond"
  ],
  "categories": [
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-06T09:43:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "poisson process",
      "invertibility",
      "applications",
      "functionals",
      "variational representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}