{
  "id": "0907.5468",
  "version": "v1",
  "published": "2009-07-31T04:43:26.000Z",
  "updated": "2009-07-31T04:43:26.000Z",
  "title": "Self-interacting diffusions IV: Rate of convergence",
  "authors": [
    "Michel Benaim",
    "Olivier Raimond"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Self-interacting diffusions are processes living on a compact Riemannian manifold defined by a stochastic differential equation with a drift term depending on the past empirical measure of the process. The asymptotics of this measure is governed by a deterministic dynamical system and under certain conditions it converges almost surely towards a deterministic measure (see Bena\\\"im, Ledoux, Raimond (2002) and Bena\\\"im, Raimond (2005)). We are interested here in the rate of this convergence. A central limit theorem is proved. In particular, this shows that greater is the interaction repelling faster is the convergence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-31T04:43:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "self-interacting diffusions",
      "convergence",
      "central limit theorem",
      "stochastic differential equation",
      "compact riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.5468B"
    }
  }
}