{
  "id": "2010.05288",
  "version": "v1",
  "published": "2020-10-11T17:20:38.000Z",
  "updated": "2020-10-11T17:20:38.000Z",
  "title": "Itô's formula for flow of measures on semimartingales",
  "authors": [
    "Xin Guo",
    "Huyên Pham",
    "Xiaoli Wei"
  ],
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "We state It\\^o's formula along a flow of probability measures associated with general semimartingales. This extends recent existing results for flow of measures on It\\^o processes. Our approach is to first prove It\\^o's formula for cylindrical polynomials and then use function approximation for the general case. Some applications to McKean- Vlasov controls of jump-diffusion processes and McKean-Vlasov singular controls are developed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-11T17:20:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H30",
      "60K35",
      "93E20"
    ],
    "keywords": [
      "itôs formula",
      "mckean-vlasov singular controls",
      "probability measures",
      "general semimartingales",
      "jump-diffusion processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}