{
  "id": "2207.09166",
  "version": "v1",
  "published": "2022-07-19T10:13:38.000Z",
  "updated": "2022-07-19T10:13:38.000Z",
  "title": "Regular subspaces of symmetric stable processes",
  "authors": [
    "Dongjian Qian",
    "Jiangang Ying",
    "Yushu Zheng"
  ],
  "comment": "12 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Roughly speaking, regular subspaces are regular Dirichlet forms which inherit the original forms with smaller domains. In this paper, regular subspaces of 1-dim symmetric $\\alpha$-stable processes are considered. The main result is that it admits proper regular subspaces if and only if $\\alpha\\in [1,2]$. Moreover, general 1-dim symmetric L\\'evy processes will also be investigated. It will be shown that whether it has proper regular subspaces is closely related to whether it has finite variation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-19T10:13:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric stable processes",
      "admits proper regular subspaces",
      "symmetric levy processes",
      "regular dirichlet forms",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}