{
  "id": "2411.07157",
  "version": "v1",
  "published": "2024-11-11T17:34:12.000Z",
  "updated": "2024-11-11T17:34:12.000Z",
  "title": "Rough differential equations in the flow approach",
  "authors": [
    "Ajay Chandra",
    "Léonard Ferdinand"
  ],
  "categories": [
    "math.PR",
    "math.CA"
  ],
  "abstract": "We show how the flow approach of Duch, with elementary differentials as coordinates, can be used to prove local well-posedness for rough stochastic differential equations driven by fractional Brownian motion with Hurst index $H > \\frac{1}{4}$. A novelty appearing here is that we use coordinates for the flow that are indexed by trees rather than multi-indices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-11T17:34:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rough differential equations",
      "flow approach",
      "rough stochastic differential equations driven",
      "fractional brownian motion",
      "elementary differentials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}