{
  "id": "math/0405152",
  "version": "v1",
  "published": "2004-05-09T09:36:15.000Z",
  "updated": "2004-05-09T09:36:15.000Z",
  "title": "Moderate deviation principle for exponentially ergodic Markov chain",
  "authors": [
    "B. Delyon",
    "A. Juditsky",
    "R. Liptser"
  ],
  "comment": "16 pg",
  "categories": [
    "math.PR"
  ],
  "abstract": "For ${1/2}<\\alpha<1$, we propose the MDP analysis for family $$ S^\\alpha_n=\\frac{1}{n^\\alpha}\\sum_{i=1}^nH(X_{i-1}), n\\ge 1, $$ where $(X_n)_{n\\ge 0}$ be a homogeneous ergodic Markov chain, $X_n\\in \\mathbb{R}^d$, when the spectrum of operator $P_x$ is continuous. The vector-valued function $H$ is not assumed to be bounded but the Lipschitz continuity of $H$ is required. The main helpful tools in our approach are Poisson equation and Stochastic Exponential; the first enables to replace the original family by $\\frac{1}{n^\\alpha}M_n$ with a martingale $M_n$ while the second to avoid the direct Laplace transform analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-09T09:36:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J27",
      "60F10"
    ],
    "keywords": [
      "exponentially ergodic markov chain",
      "moderate deviation principle",
      "direct laplace transform analysis",
      "homogeneous ergodic markov chain",
      "mdp analysis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5152D"
    }
  }
}