{
  "id": "2312.07084",
  "version": "v1",
  "published": "2023-12-12T09:05:35.000Z",
  "updated": "2023-12-12T09:05:35.000Z",
  "title": "A probabilistic representation of the derivative of a one dimensional killed diffusion semigroup and associated Bismut-Elworthy-Li formula",
  "authors": [
    "Dan Crisan",
    "Arturo Kohatsu-Higa"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We provide a probabilistic representation for the derivative of the semigroup corresponding to a diffusion process killed at the boundary of a half interval. In particular, we show that the derivative of the semi-group can be expressed as the expected value of a functional of a reflected diffusion process. Furthermore, as an application, we obtain a Bismut-Elworthy-Li formula which is also valid at the boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-12T09:05:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60J60",
      "60G40"
    ],
    "keywords": [
      "dimensional killed diffusion semigroup",
      "associated bismut-elworthy-li formula",
      "probabilistic representation",
      "derivative",
      "half interval"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}