{
  "id": "1506.02895",
  "version": "v1",
  "published": "2015-06-09T13:13:52.000Z",
  "updated": "2015-06-09T13:13:52.000Z",
  "title": "Renewal structure and local time for diffusions in random environment",
  "authors": [
    "Pierre Andreoletti",
    "Grégoire Vechambre",
    "Alexis Devulder"
  ],
  "comment": "39 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a one-dimensional diffusion $X$ in a drifted Brownian potential $W\\_\\kappa$, with $ 0\\textless{}\\kappa\\textless{}1$, and focus on the behavior of the local times $(\\mathcal{L}(t,x),x)$ of $X$ before time $t\\textgreater{}0$. In particular we characterize the limit law of the supremum of the local time, as well as the position of the favorite sites. These limits can be written explicitly from a two dimensional stable L{\\'e}vy process. Our analysis is based on the study of an extension of the renewal structure which is deeply involved in the asymptotic behavior of $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-09T13:13:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local time",
      "renewal structure",
      "random environment",
      "vy process",
      "one-dimensional diffusion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150602895A"
    }
  }
}