{
  "id": "2206.07159",
  "version": "v1",
  "published": "2022-06-14T20:39:21.000Z",
  "updated": "2022-06-14T20:39:21.000Z",
  "title": "Weak solutions for stochastic differential equations with additive fractional noise",
  "authors": [
    "Pedro J. Catuogno",
    "Diego S. Ledesma"
  ],
  "comment": "10pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We give a new approach to prove the existence of a weak solution of \\[dx_t = f(t,x_t)dt + g(t)dB^H_t\\] where $B^H_t$ is a fractional Brownian motion with values in a separable Hilbert space for suitable functions $f$ and $g$. Our idea is to use the implicit function theorem and the scaling property of the fractional Brownian motion in order to obtain a weak solution for this equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-14T20:39:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60G22",
      "60G18",
      "G.3"
    ],
    "keywords": [
      "weak solution",
      "stochastic differential equations",
      "additive fractional noise",
      "fractional brownian motion",
      "implicit function theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}