{
  "id": "1703.02782",
  "version": "v1",
  "published": "2017-03-08T10:49:12.000Z",
  "updated": "2017-03-08T10:49:12.000Z",
  "title": "Rough path properties for local time of symmetric $α$ stable process",
  "authors": [
    "Qingfeng Wang",
    "Huaizhong Zhao"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we first prove that the local time associated with symmetric $\\alpha$-stable processes is of bounded $p$-variation for any $p>\\frac{2}{\\alpha-1}$ partly based on Barlow's estimation of the modulus of the local time of such processes.\\,\\,The fact that the local time is of bounded $p$-variation for any $p>\\frac{2}{\\alpha-1}$ enables us to define the integral of the local time $\\int_{-\\infty}^{\\infty}\\triangledown_-^{\\alpha-1}f(x)d_x L_t^x$ as a Young integral for less smooth functions being of bounded $q$-varition with $1\\leq q<\\frac{2}{3-\\alpha}$. When $q\\geq \\frac{2}{3-\\alpha}$, Young's integration theory is no longer applicable. However, rough path theory is useful in this case. The main purpose of this paper is to establish a rough path theory for the integration with respect to the local times of symmetric $\\alpha$-stable processes for $\\frac{2}{3-\\alpha}\\leq q< 4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-08T10:49:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G52",
      "60J55",
      "60H05"
    ],
    "keywords": [
      "local time",
      "rough path properties",
      "stable process",
      "rough path theory",
      "youngs integration theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}