{
  "id": "1104.1464",
  "version": "v3",
  "published": "2011-04-08T00:54:32.000Z",
  "updated": "2012-02-06T23:06:23.000Z",
  "title": "Towards zero variance estimators for rare event probabilities",
  "authors": [
    "Michel Broniatowski",
    "Virgile Caron"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events E_{n}:=(f(X_{1})+...+f(X_{n}))\\inA_{n} where the summands are i.i.d. and E_{n} is a large or moderate deviation event. The approximation of the conditional density of the real r.v's X_{i} 's, for 1\\leqi\\leqk_{n} with repect to E_{n} on long runs, when k_{n}/n\\to1, is handled. The maximal value of k compatible with a given accuracy is discussed; algorithms and simulated results are presented.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-02-06T23:06:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60-08",
      "65C05"
    ],
    "keywords": [
      "rare event probabilities",
      "zero variance estimators",
      "conditional density",
      "moderate deviation event",
      "improving importance sampling estimators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.1464B"
    }
  }
}