{
  "id": "math/0603021",
  "version": "v1",
  "published": "2006-03-01T12:57:03.000Z",
  "updated": "2006-03-01T12:57:03.000Z",
  "title": "Deviation bounds for additive functionals of Markov process",
  "authors": [
    "Patrick Cattiaux",
    "Arnaud Guillin"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we derive non asymptotic deviation bounds for $$\\P_\\nu (|\\frac 1t \\int_0^t V(X_s) ds - \\int V d\\mu | \\geq R)$$ where $X$ is a $\\mu$ stationary and ergodic Markov process and $V$ is some $\\mu$ integrable function. These bounds are obtained under various moments assumptions for $V$, and various regularity assumptions for $\\mu$. Regularity means here that $\\mu$ may satisfy various functional inequalities (F-Sobolev, generalized Poincar\\'e etc...).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-01T12:57:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60J25"
    ],
    "keywords": [
      "additive functionals",
      "derive non asymptotic deviation bounds",
      "ergodic markov process",
      "moments assumptions",
      "regularity assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3021C"
    }
  }
}