{
  "id": "2304.01449",
  "version": "v1",
  "published": "2023-04-04T01:45:21.000Z",
  "updated": "2023-04-04T01:45:21.000Z",
  "title": "Wong-Zakai approximation of density functions",
  "authors": [
    "Yuzuru Inahama"
  ],
  "comment": "35 pages, no figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we prove the Wong-Zakai approximation of probability density functions of solutions at a fixed time of rough differential equations driven by fractional Brownian rough path with Hurst parameter $H$ $(1/4 <H \\leq 1/2)$. Besides rough path theory, we use Hu-Watanabe's approximation theorem in the framework of Watanabe's distributional Malliavin calculus. When $H=1/2$, the random rough differential equations coincide with the corresponding Stratonovich-type stochastic differential equations. Even for that case, our main result seems new.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-04T01:45:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H35",
      "60L90",
      "60H07",
      "60G22"
    ],
    "keywords": [
      "wong-zakai approximation",
      "density functions",
      "random rough differential equations coincide",
      "watanabes distributional malliavin calculus",
      "fractional brownian rough path"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}