{
  "id": "math/0503070",
  "version": "v1",
  "published": "2005-03-04T01:47:28.000Z",
  "updated": "2005-03-04T01:47:28.000Z",
  "title": "Examples of moderate deviation principle for diffusion processes",
  "authors": [
    "A. Guillin}",
    "R. Liptser"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Taking into account some likeness of moderate deviations (MD) and central limit theorems (CLT), we develop an approach, which made a good showing in CLT, for MD analysis of a family $$ S^\\kappa_t=\\frac{1}{t^\\kappa}\\int_0^tH(X_s)ds, \\ t\\to\\infty $$ for an ergodic diffusion process $X_t$ under $0.5<\\kappa<1$ and appropriate $H$. We mean a decomposition with ``corrector'': $$ \\frac{1}{t^\\kappa}\\int_0^tH(X_s)ds={\\rm corrector}+\\frac{1}{t^\\kappa}\\underbrace{M_t}_{\\rm martingale}. $$ and show that, as in the CLT analysis, the corrector is negligible but in the MD scale, and the main contribution in the MD brings the family ``$ \\frac{1}{t^\\kappa}M_t, t\\to\\infty. $'' Starting from Bayer and Freidlin, \\cite{BF}, and finishing by Wu's papers \\cite{Wu1}-\\cite{WuH}, in the MD study Laplace's transform dominates. In the paper, we replace the Laplace technique by one, admitting to give the conditions, providing the MD, in terms of ``drift-diffusion'' parameters and $H$. However, a verification of these conditions heavily depends on a specificity of a diffusion model. That is why the paper is named ``Examples ...''.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-04T01:47:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60J27"
    ],
    "keywords": [
      "moderate deviation principle",
      "diffusion processes",
      "md study laplaces transform dominates",
      "ergodic diffusion process",
      "central limit theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3070G"
    }
  }
}