{
  "id": "1605.06911",
  "version": "v1",
  "published": "2016-05-23T07:11:18.000Z",
  "updated": "2016-05-23T07:11:18.000Z",
  "title": "A representation for the derivative with respect to the initial data of the solution of an SDE with a non-regular drift and a Gaussian noise",
  "authors": [
    "Olga Aryasova",
    "Andrey Pilipenko"
  ],
  "comment": "26 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a multidimensional SDE with a Gaussian noise and a drift vector being a vector function of bounded variation. We prove the existence of generalized derivative of the solution with respect to the initial conditions and represent the derivative as a solution of a linear SDE with coefficients depending on the initial process. The representation obtained is a natural generalization of the expression for the derivative in the smooth case. The theory of continuous additive functionals is used.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-23T07:11:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60H10"
    ],
    "keywords": [
      "gaussian noise",
      "initial data",
      "non-regular drift",
      "representation",
      "derivative"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}