{
  "id": "1801.05936",
  "version": "v1",
  "published": "2018-01-18T04:56:25.000Z",
  "updated": "2018-01-18T04:56:25.000Z",
  "title": "Gradient Estimates and Ergodicity for SDEs Driven by Multiplicative Lévy Noises via Coupling",
  "authors": [
    "Mingjie Liang",
    "Jian Wang"
  ],
  "comment": "34 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider SDEs driven by multiplicative pure jump L\\'{e}vy noises, where L\\'evy processes are not necessarily comparable to $\\alpha$-stable-like processes. By assuming that the SDE has a unique solution, we obtain gradient estimates of the associated semigroup when the drift term is locally H\\\"{o}lder continuous, and we establish the ergodicity of the process both in the $L^1$-Wasserstein distance and the total variation, when the coefficients are dissipative for large distances. The proof is based on a new explicit Markov coupling for SDEs driven by multiplicative pure jump L\\'{e}vy noises, which is derived for the first time in this paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-18T04:56:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sdes driven",
      "multiplicative lévy noises",
      "gradient estimates",
      "ergodicity",
      "multiplicative pure jump"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}