{
  "id": "1206.7063",
  "version": "v1",
  "published": "2012-06-29T16:09:30.000Z",
  "updated": "2012-06-29T16:09:30.000Z",
  "title": "Weak and strong approximations of reflected diffusions via penalization methods",
  "authors": [
    "Leszek Slominski"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study approximations of reflected It\\^o diffusions on convex subsets $D$ of $\\Rd$ by solutions of stochastic differential equations with penalization terms. We assume that the diffusion coefficients are merely measurable (possibly discontinuous) functions. In the case of Lipschitz continuous coefficients we give the rate of $L^p$ approximation for every $p\\geq1$. We prove that if $D$ is a convex polyhedron then the rate is $O((\\frac{\\ln n}n)^{1/2})$, and in the general case the rate is $O((\\frac{\\ln n}n)^{1/4})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-29T16:09:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "strong approximations",
      "penalization methods",
      "reflected diffusions",
      "stochastic differential equations",
      "general case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.7063S"
    }
  }
}