{
  "id": "1807.00363",
  "version": "v1",
  "published": "2018-07-01T18:11:33.000Z",
  "updated": "2018-07-01T18:11:33.000Z",
  "title": "On invariant probability measures of regime-switching diffusion processes with singular drifts",
  "authors": [
    "Shao-Qin Zhang"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "For regime-switching diffusions processes with singular drifts, we introduce integrability conditions involving a nice reference probability measure and the $Q$-matrix of the jump part to study the existence of the invariant probability measures. Consequently, the generator of the regime-switching diffusions process has an extension in the $L^1$-space w.r.t the invariant probability measure to be a generator of $C_0$-semigroup. Moreover, we prove the uniqueness of the extension. Regularities and the uniqueness of the invariant probability density w.r.t the nice reference probability measure are also considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-01T18:11:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H60",
      "60J05"
    ],
    "keywords": [
      "invariant probability measure",
      "regime-switching diffusion processes",
      "singular drifts",
      "nice reference probability measure",
      "regime-switching diffusions process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}