{
  "id": "2306.02803",
  "version": "v1",
  "published": "2023-06-05T11:57:08.000Z",
  "updated": "2023-06-05T11:57:08.000Z",
  "title": "Existence of density functions for SDEs driven by pure-jump processes",
  "authors": [
    "Takuya Nakagawa",
    "Ryoichi Suzuki"
  ],
  "comment": "21 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We verify the existence of density functions of the running maximum of a stochastic differential equation (SDE) driven by a Brownian motion and a non-truncated stable process. This is proved by the existence of density functions of the running maximum of Wiener-Poisson functionals resulting from Bismut's approach to Malliavin calculus for jump processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-05T11:57:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60G52",
      "60H07"
    ],
    "keywords": [
      "density functions",
      "pure-jump processes",
      "sdes driven",
      "running maximum",
      "stochastic differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}