{
  "id": "1305.7174",
  "version": "v3",
  "published": "2013-05-30T17:38:40.000Z",
  "updated": "2014-09-02T15:45:16.000Z",
  "title": "On weak uniqueness for some degenerate SDEs by global $L^p$ estimates",
  "authors": [
    "Enrico Priola"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We prove uniqueness in law for possibly degenerate SDEs having a linear part in the drift term. Diffusion coefficients corresponding to non-degenerate directions of the noise are assumed to be continuous. When the diffusion part is constant we recover the classical degenerate Ornstein-Uhlenbeck process which only has to satisfy the H\\\"ormander hypoellipticity condition. In the proof we use global $L^p$-estimates for hypoelliptic Ornstein-Uhlenbeck operators recently proved in Bramanti-Cupini-Lanconelli-Priola (Math. Z. 266 (2010)) and adapt the localization procedure introduced by Stroock and Varadhan. Appendix contains a quite general localization principle for martingale problems.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-18T17:20:20.000Z",
      "comment": "Typos have been fixed; more details have been added",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-09-02T15:45:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "degenerate sdes",
      "weak uniqueness",
      "quite general localization principle",
      "hypoelliptic ornstein-uhlenbeck operators",
      "classical degenerate ornstein-uhlenbeck process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.7174P"
    }
  }
}