{
  "id": "1906.08426",
  "version": "v1",
  "published": "2019-06-20T03:15:33.000Z",
  "updated": "2019-06-20T03:15:33.000Z",
  "title": "Long time behavior of Levy-driven Ornstein-Uhlenbeck process with regime-switchin",
  "authors": [
    "Zhong-Wei Liao",
    "Jinghai Shao"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this work we investigate the long time behavior of the Ornstein-Uhlenbeck process driven by Levy noise with regime-switching. We provide explicit criteria on the transience and recurrence of this process. Contrasted with the Ornstein-Uhlenbeck process driven simply by Brownian motion, whose stationary distribution must be light-tailed, both the jumps caused by the Levy noise and regime-switching described by Markov chain can derive the heavy-tailed property of the stationary distribution. In this work, the different role played by Levy measure and regime-switching process is clearly characterized.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-20T03:15:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J75",
      "60K37",
      "60J60"
    ],
    "keywords": [
      "long time behavior",
      "levy-driven ornstein-uhlenbeck process",
      "ornstein-uhlenbeck process driven",
      "levy noise",
      "regime-switchin"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}