{
  "id": "1902.09111",
  "version": "v1",
  "published": "2019-02-25T07:00:48.000Z",
  "updated": "2019-02-25T07:00:48.000Z",
  "title": "Complex Wiener-Itô Chaos Decomposition Revisited",
  "authors": [
    "Yong CHEN",
    "Yong LIU"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, some properties of complex Wiener-It\\^o multiple integrals and complex Ornstein-Uhlenbeck operators and semigroups are obtained. Those include Stroock's formula, Hu-Meyer formula, Clark-Ocone formula and the hypercontractivity of complex Ornstein-Uhlenbeck semigroups. As an application, several expansions of the fourth moments of complex Wiener-It\\^o multiple integrals are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-25T07:00:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H07",
      "60F25"
    ],
    "keywords": [
      "chaos decomposition",
      "multiple integrals",
      "complex ornstein-uhlenbeck operators",
      "complex ornstein-uhlenbeck semigroups",
      "stroocks formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}