{
  "id": "2412.15820",
  "version": "v1",
  "published": "2024-12-20T12:02:33.000Z",
  "updated": "2024-12-20T12:02:33.000Z",
  "title": "The particle approximation of quasi-stationary distributions. Part~I: concentration bounds in the uniform case",
  "authors": [
    "Lucas Journel",
    "Mathias Rousset"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study mean-field particle approximations of normalized Feynman-Kac semi-groups, usually called Fleming-Viot or Feynman-Kac particle systems. Assuming various large time stability properties of the semi-group uniformly in the initial condition, we provide explicit time-uniform $L^p$ and exponential bounds (a new result) with the expected rate in terms of sample size. This work is based on a stochastic backward error analysis (similar to the classical concept of numerical analysis) of the measure-valued Markov particle estimator, an approach that simplifies methods previously used for time-uniform $L^p$ estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-20T12:02:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasi-stationary distributions",
      "concentration bounds",
      "uniform case",
      "study mean-field particle approximations",
      "large time stability properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}