{
  "id": "1808.07086",
  "version": "v1",
  "published": "2018-08-21T19:03:11.000Z",
  "updated": "2018-08-21T19:03:11.000Z",
  "title": "An Approximation Scheme for Quasistationary Distributions of Killed Diffusions",
  "authors": [
    "Andi Q. Wang",
    "Gareth O. Roberts",
    "David Steinsaltz"
  ],
  "comment": "20 pages, 1 figure",
  "categories": [
    "math.PR",
    "stat.ME"
  ],
  "abstract": "In this paper we study the asymptotic behavior of the normalized weighted empirical occupation measures of a diffusion process on a compact manifold which is also killed at a given rate and regenerated at a random location, distributed according to the weighted empirical occupation measure. We show that the weighted occupation measures almost surely comprise an asymptotic pseudo-trajectory for a certain deterministic measure-valued semiflow, after suitably rescaling the time, and that with probability one they converge to the quasistationary distribution of the killed diffusion. These results provide theoretical justification for a scalable quasistationary Monte Carlo method for sampling from Bayesian posterior distributions in large data settings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-21T19:03:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B12",
      "60J60",
      "37C50",
      "65C05"
    ],
    "keywords": [
      "quasistationary distribution",
      "weighted empirical occupation measure",
      "killed diffusion",
      "approximation scheme",
      "scalable quasistationary monte carlo method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}