{
  "id": "1402.5079",
  "version": "v1",
  "published": "2014-02-20T17:22:38.000Z",
  "updated": "2014-02-20T17:22:38.000Z",
  "title": "Strong completeness for a class of stochastic differential equations with irregular coefficients",
  "authors": [
    "Xin Chen",
    "Xue-Mei Li"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove the strong completeness for a class of non-degenerate SDEs, whose coefficients are not necessarily uniformly elliptic nor locally Lipschitz continuous nor bounded. Moreover, for each $t$, the solution flow $F_t$ is weakly differentiable and for each $p>0$ there is a positive number $T(p)$ such that for all $t<T(p)$, the solution flow $F_t(\\cdot)$ belongs to the Sobolev space $W_{\\loc}^{1,p}$. The main tool for this is the approximation of the associated derivative flow equations. As an application a differential formula is also obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-20T17:22:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic differential equations",
      "strong completeness",
      "irregular coefficients",
      "solution flow",
      "associated derivative flow equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.5079C"
    }
  }
}