{
  "id": "1811.07101",
  "version": "v2",
  "published": "2018-11-17T05:02:58.000Z",
  "updated": "2019-10-08T00:40:25.000Z",
  "title": "Probability density function of SDEs with unbounded and path--dependent drift coefficient",
  "authors": [
    "Dai Taguchi",
    "Akihiro Tanaka"
  ],
  "comment": "49 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we first prove that the existence of a solution of SDEs under the assumptions that the drift coefficient is of linear growth and path--dependent, and diffusion coefficient is bounded, uniformly elliptic and H\\\"older continuous. We apply Gaussian upper bound for a probability density function of a solution of SDE without drift coefficient and local Novikov condition, in order to use Maruyama--Girsanov transformation. The aim of this paper is to prove the existence with explicit representations (under linear/super--linear growth condition), Gaussian two--sided bound and H\\\"older continuity (under sub--linear growth condition) of a probability density function of a solution of SDEs with path--dependent drift coefficient. As an application of explicit representation, we provide the rate of convergence for an Euler--Maruyama (type) approximation, and an unbiased simulation scheme.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2019-10-08T00:40:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65C30",
      "62G07",
      "35K08",
      "60H35"
    ],
    "keywords": [
      "probability density function",
      "path-dependent drift coefficient",
      "explicit representation",
      "linear/super-linear growth condition",
      "apply gaussian upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}