{
  "id": "2304.08088",
  "version": "v1",
  "published": "2023-04-17T09:03:38.000Z",
  "updated": "2023-04-17T09:03:38.000Z",
  "title": "An improved complex fourth moment theorem",
  "authors": [
    "Huiping Chen",
    "Yong Chen",
    "Yong Liu"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "For a series of univariate or multivariate complex multiple Wiener-It\\^o integrals, we appreciably improve the previously known contractions condition of complex Fourth Moment Theorem (FMT) and present a fourth moment type Berry-Ess\\'een bound under Wasserstein distance. Note that in some special cases of univariate complex multiple Wiener-It\\^o integral, the Berry-Ess\\'een bound we acquired is optimal. A remarkable fact is that the Berry-Ess\\'een bound of multivariate complex multiple Wiener-It\\^o integral is related to the partially order of the index of the complex multiple Wiener-It\\^o integral, which has no real counterparts as far as we know. As an application, we explore the asymptotic property for the numerator of a ratio process which originates from the classical Chandler wobble model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-17T09:03:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60G15",
      "60H05"
    ],
    "keywords": [
      "complex fourth moment theorem",
      "multivariate complex multiple",
      "fourth moment type berry-esseen bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}