{
  "id": "2211.07239",
  "version": "v1",
  "published": "2022-11-14T09:55:14.000Z",
  "updated": "2022-11-14T09:55:14.000Z",
  "title": "On partially observed jump diffusions III. Regularity of the filtering density",
  "authors": [
    "Fabian Germ",
    "István Gyöngy"
  ],
  "comment": "43 pages",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "The filtering equations associated to a partially observed jump diffusion model $(Z_t)_{t\\in [0,T]}=(X_t,Y_t)_{t\\in [0,T]}$, driven by Wiener processes and Poisson martingale measures are considered. Building on results from two preceding articles on the filtering equations, the regularity of the conditional density of the signal $X_t$, given observations $(Y_s)_{s\\in [0,t]}$, is investigated, when the conditional density of $X_0$ given $Y_0$ exists and belongs to a Sobolev space, and the coefficients satisfy appropriate smoothness and growth conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-14T09:55:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G35",
      "60H15",
      "60G57",
      "60H20"
    ],
    "keywords": [
      "filtering density",
      "regularity",
      "coefficients satisfy appropriate smoothness",
      "conditional density",
      "poisson martingale measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}