{
  "id": "1606.03850",
  "version": "v1",
  "published": "2016-06-13T08:06:38.000Z",
  "updated": "2016-06-13T08:06:38.000Z",
  "title": "Absolute continuity of the law for solutions of stochastic differential equations with boundary noise",
  "authors": [
    "Stefano Bonaccorsi",
    "Margherita Zanella"
  ],
  "comment": "25 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study existence and regularity of the density for the solution $u(t,x)$ (with fixed $t > 0$ and $x \\in D$) of the heat equation in a bounded domain $D \\subset \\mathbb R^d$ driven by a stochastic inhomogeneous Neumann boundary condition with stochastic term. The stochastic perturbation is given by a fractional Brownian motion process. Under suitable regularity assumptions on the coefficients, by means of tools from the Malliavin calculus, we prove that the law of the solution has a smooth density with respect to the Lebesgue measure in $\\mathbb R$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-13T08:06:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H07"
    ],
    "keywords": [
      "stochastic differential equations",
      "boundary noise",
      "absolute continuity",
      "fractional brownian motion process",
      "stochastic inhomogeneous neumann boundary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}