{
  "id": "1709.02141",
  "version": "v1",
  "published": "2017-09-07T08:51:39.000Z",
  "updated": "2017-09-07T08:51:39.000Z",
  "title": "continuous time random walk as a random walk in a random environment",
  "authors": [
    "Ofer Busani"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that for a weakly dense subset of the domain of attraction of a positive stable random variable of index $0<\\alpha<1$($DOA\\left(\\alpha\\right))$ the functional stable convergence is a time-changed renewal convergence of distribution of finite mean. Applied to Continuous Time Random Walk(CTRW) \\'{a} la Montroll and Wiess we show that CTRW with renewal times in a weakly dense set of $DOA\\left(\\alpha\\right)$ can be realized as random walk in a random environment. We find the quenched limit and give a bound on the error of the approximation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-07T08:51:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous time random walk",
      "random environment",
      "weakly dense subset",
      "weakly dense set",
      "renewal times"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}