{
  "id": "1809.06840",
  "version": "v1",
  "published": "2018-09-18T17:38:09.000Z",
  "updated": "2018-09-18T17:38:09.000Z",
  "title": "On solvability of integro-differential equations",
  "authors": [
    "Marta De León-Contreras",
    "István Gyöngy",
    "Sizhou Wu"
  ],
  "comment": "37 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "A class of (possibly) degenerate integro-differential equations of parabolic type is considered, which includes the Kolmogorov equations for jump diffusions. Existence and uniqueness of the solutions are established in Bessel potential spaces and in Sobolev-Slobodeckij spaces. Generalisations to stochastic integro-differential equations, arising in filtering theory of jump diffusions, will be given in a forthcoming paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-18T17:38:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "45K05",
      "35R09",
      "47G20"
    ],
    "keywords": [
      "solvability",
      "jump diffusions",
      "stochastic integro-differential equations",
      "bessel potential spaces",
      "degenerate integro-differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}