{
  "id": "math/0702364",
  "version": "v3",
  "published": "2007-02-13T12:11:29.000Z",
  "updated": "2007-10-02T14:09:01.000Z",
  "title": "Smooth densities for stochastic differential equations with jumps",
  "authors": [
    "Thomas Cass"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a solution to a generic Markovian jump diffusion and show that for positive times the law of the solution process has a smooth density with respect to Lebesgue measure under a uniform version of Hoermander's conditions. Unlike previous results in the area the result covers a class of infinite activity jump processes. The result is accompolished by using carefully crafted refinements to the classical arguments used in proving smoothness of density via Malliavin calculus. In particular, a key ingredient is provided by our proof that the semimartinagle inequality of Norris persists for discontinuous semimartingales when the jumps of the semimartinagale are small.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-10-02T14:09:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H07",
      "60H15"
    ],
    "keywords": [
      "stochastic differential equations",
      "smooth density",
      "generic markovian jump diffusion",
      "infinite activity jump processes",
      "hoermanders conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2364C"
    }
  }
}