{
  "id": "1904.08620",
  "version": "v1",
  "published": "2019-04-18T07:45:30.000Z",
  "updated": "2019-04-18T07:45:30.000Z",
  "title": "Stochastic approximation of quasi-stationary distributions for diffusion processes in a bounded domain",
  "authors": [
    "Michel Benaïm",
    "Nicolas Champagnat",
    "Denis Villemonais"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a random process with reinforcement, which evolves following the dynamics of a given diffusion process in a bounded domain and is resampled according to its occupation measure when it reaches the boundary. We show that its occupation measure converges to the unique quasi-stationary distribution of the diffusion process absorbed at the boundary of the domain. Our proofs use recent results in the theory of quasi-stationary distributions and stochastic approximation techniques.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-18T07:45:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diffusion process",
      "bounded domain",
      "unique quasi-stationary distribution",
      "stochastic approximation techniques",
      "occupation measure converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}