{
  "id": "2106.14825",
  "version": "v1",
  "published": "2021-06-28T16:02:30.000Z",
  "updated": "2021-06-28T16:02:30.000Z",
  "title": "Central Limit Theorem for product of dependent random variables",
  "authors": [
    "JunTao Duan",
    "Ionel Popescu",
    "Fan Zhou"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Given $\\{X_k\\}$ is a martingale difference sequence. And given another $\\{Y_k\\}$ which has dependency within the sequence. Assume $\\{X_k\\}$ is independent with $\\{Y_k\\}$, we study the properties of the sums of product of two sequences $\\sum_{k=1}^{n} X_k Y_k$. We obtain product-CLT, a modification of classical central limit theorem, which can be useful in the study of random projections. We also obtain the rate of convergence which is similar to the Berry-Essen theorem in the classical CLT.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-28T16:02:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dependent random variables",
      "martingale difference sequence",
      "classical central limit theorem",
      "random projections",
      "berry-essen theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}