{
  "annotation_id": "57e68aaa-b05e-410f-94b0-66a36709ea19",
  "date_created": "2026-02-17T05:53:24.056000Z",
  "date_modified": "2026-02-17T05:53:24.056000Z",
  "file_hash": "c047280d45e72a99e21e0d3283c39881ac9ae77f5cabd47ccbbeb33aa30e4664",
  "private": false,
  "record": {
    "abstract": "We prove that, under the H\\\"ormander criterion on an It\\^{o} process, all its martingale observables are smooth. As a consequence, we also obtain a generalized Feynman-Kac formula providing smooth solutions to certain PDE boundary-value problems, while allowing for degenerate diffusions as well as boundary stopping (under very mild boundary regularity assumptions). We also highlight an application to a question posed on Schramm-Loewner evolutions, by making certain Girsanov transform martingales accessible via It\\^{o} calculus.",
    "arxiv_id": "2601.10539",
    "authors": [
      "Alex Karrila",
      "Lauri Viitasaari"
    ],
    "categories": [
      "math.PR",
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Smoothness of martingale observables and generalized Feynman-Kac formulas",
    "url": "https://arxiv.org/abs/2601.10539",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "44fe908d-d4be-4a6a-bac9-a9ff20149683",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}