{
  "id": "2001.07794",
  "version": "v1",
  "published": "2020-01-21T22:03:59.000Z",
  "updated": "2020-01-21T22:03:59.000Z",
  "title": "Convergence to quasi-stationarity through Poincaré inequalities and Bakry-Emery criteria",
  "authors": [
    "William Oçafrain"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper aims to provide some tools coming from functional inequalities to deal with quasi-stationarity for absorbed Markov processes. First, it is shown how a Poincar\\'e inequality related to a suitable Doob transform entails exponential convergence of conditioned distributions to a quasi-stationary distribution in total variation and in $1$-Wasserstein distance. A special attention is paid to multi-dimensional diffusion processes, for which the aforementioned Poincar\\'e inequality is implied by an easier-to-check Bakry-\\'{E}mery condition depending on the right eigenvector for the sub-Markovian generator, which is not always known. Under additional assumptions on the potential, it is possible to bypass this lack of knowledge showing that exponential quasi-ergodicity is entailed by the classical Bakry-\\'{E}mery condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-21T22:03:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bakry-emery criteria",
      "quasi-stationarity",
      "doob transform entails exponential convergence",
      "suitable doob transform entails exponential",
      "poincare inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}