{
  "id": "1708.04659",
  "version": "v1",
  "published": "2017-08-15T19:42:09.000Z",
  "updated": "2017-08-15T19:42:09.000Z",
  "title": "Rough differential equations with power type nonlinearities",
  "authors": [
    "Prakash Chakraborty",
    "Samy Tindel"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this note we consider differential equations driven by a signal $x$ which is $\\gamma$-H\\\"older with $\\gamma>1/3$, and is assumed to possess a lift as a rough path. Our main point is to obtain existence of solutions when the coefficients of the equation behave like power functions of the form $|\\xi|^{\\kappa}$ with $\\kappa\\in(0,1)$. Two different methods are used in order to construct solutions: (i) In a 1-d setting, we resort to a rough version of Lamperti's transform. (ii) For multidimensional situations, we quantify some improved regularity estimates when the solution approaches the origin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-15T19:42:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rough differential equations",
      "power type nonlinearities",
      "differential equations driven",
      "main point",
      "solution approaches"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}