{
  "id": "1912.09108",
  "version": "v1",
  "published": "2019-12-19T10:28:25.000Z",
  "updated": "2019-12-19T10:28:25.000Z",
  "title": "Lyapunov-type Conditions for Non-strong Ergodicity of Markov Processes",
  "authors": [
    "Yong-Hua Mao",
    "Tao Wang"
  ],
  "comment": "15 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We present Lyapunov-type conditions for non-strong ergodicity of Markov processes. Some concrete models are discussed including diffusion processes on Riemannian manifolds and Ornstein-Uhlenbeck processes driven by symmetric $\\alpha$-stable processes. For SDE driven by $\\alpha$-stable process ($\\alpha\\in (0,2]$) with polynomial drift, the strong ergodicity or not is independent on $\\alpha$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-19T10:28:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lyapunov-type conditions",
      "non-strong ergodicity",
      "markov processes",
      "ornstein-uhlenbeck processes driven",
      "stable process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}