{
  "id": "1107.3432",
  "version": "v3",
  "published": "2011-07-18T13:33:11.000Z",
  "updated": "2015-11-26T01:47:02.000Z",
  "title": "Moderate Deviation Principle for dynamical systems with small random perturbation",
  "authors": [
    "Yutao ma",
    "Ran Wang",
    "Liming Wu"
  ],
  "comment": "The result in this paper is covered by \" A. Guillin. Averaging principle of SDE with small diffusion: moderate deviations. Ann. Probab. 31 (2003), no. 1, 413–443.\"",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider the stochastic differential equation in $\\rr^d$ dX^{\\e}_t&=b(X^{\\e}_t)dt+\\sqrt{\\e}\\sigma(X^\\e_t)dB_t X^{\\e}_0&=x_0,\\quad x_0\\in\\rr^d where $b:\\rr^d\\rightarrow\\rr^d$ is $C^1$ such that $<x,b(x)> \\leq C(1+|x|^2)$, $\\sigma:\\rr^d\\rightarrow \\MM(d\\times n)$ is locally Lipschitzian with linear growth, and $B_t$ is a standard Brownian motion taking values in $\\rr^n$. Freidlin-Wentzell's theorem gives the large deviation principle for $X^\\e$ for small $\\e$. In this paper we establish its moderate deviation principle.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-12-20T07:09:47.000Z",
      "comment": "This paper is included in another one",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-11-26T01:47:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60H10"
    ],
    "keywords": [
      "moderate deviation principle",
      "small random perturbation",
      "dynamical systems",
      "large deviation principle",
      "stochastic differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.3432M"
    }
  }
}