{
  "id": "1212.5845",
  "version": "v1",
  "published": "2012-12-23T23:54:49.000Z",
  "updated": "2012-12-23T23:54:49.000Z",
  "title": "Asymptotic expansion for the quadratic form of the diffusion process",
  "authors": [
    "Nakahiro Yoshida"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1210.3680",
  "categories": [
    "math.PR"
  ],
  "abstract": "In [8], asymptotic expansion of the martingale with mixed normal limit was provided. The expansion formula is expressed by the adjoint of a random symbol with coefficients described by the Malliavin calculus, differently from the standard invariance principle. As an application, an asymptotic expansion for a quadratic form of a diffusion process was derived in the same paper. This article gives some details of the derivation, after a short review of the martingale expansion in mixed normal limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-23T23:54:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic expansion",
      "diffusion process",
      "quadratic form",
      "mixed normal limit",
      "standard invariance principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.5845Y"
    }
  }
}