{
  "id": "1106.5106",
  "version": "v1",
  "published": "2011-06-25T06:46:14.000Z",
  "updated": "2011-06-25T06:46:14.000Z",
  "title": "Stochastic algorithms for computing means of probability measures",
  "authors": [
    "Marc Arnaudon",
    "Clément Dombry",
    "Anthony Phan",
    "Le Yang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that the functional to minimize is regular around the p-mean, we prove that a natural renormalization of the inhomogeneous Markov chain converges in law into an inhomogeneous diffusion process. We give an explicit expression of this process, as well as its local characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-25T06:46:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probability measure",
      "stochastic algorithm",
      "computing means",
      "inhomogeneous markov chain converges",
      "regular geodesic ball"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.5106A"
    }
  }
}