{
  "id": "1004.3043",
  "version": "v1",
  "published": "2010-04-18T17:43:39.000Z",
  "updated": "2010-04-18T17:43:39.000Z",
  "title": "A Note on the Smoluchowski-Kramers Approximation for the Langevin Equation with Reflection",
  "authors": [
    "Konstantinos Spiliopoulos"
  ],
  "comment": "14 pages, 2 figures",
  "journal": "Stochastics and Dynamics, Vol. 7, No. 2, June 2007 , 141-153",
  "doi": "10.1142/S0219493707002001",
  "categories": [
    "math.PR"
  ],
  "abstract": "According to the Smoluchowski-Kramers approximation, the solution of the equation ${\\mu}\\ddot{q}^{\\mu}_t=b(q^{\\mu}_t)-\\dot{q}^{\\mu}_t+{\\Sigma}(q^{\\mu}_t)\\dot{W}_t, q^{\\mu}_0=q, \\dot{q}^{\\mu}_0=p$ converges to the solution of the equation $\\dot{q}_t=b(q_t)+{\\Sigma}(q_t)\\dot{W}_t, q_0=q$ as {\\mu}->0. We consider here a similar result for the Langevin process with elastic reflection on the boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-18T17:43:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60J99",
      "37A50"
    ],
    "keywords": [
      "smoluchowski-kramers approximation",
      "langevin equation",
      "similar result",
      "langevin process"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.3043S"
    }
  }
}