{
  "id": "2403.18304",
  "version": "v1",
  "published": "2024-03-27T06:59:20.000Z",
  "updated": "2024-03-27T06:59:20.000Z",
  "title": "Complete moment convergence of moving average processes for $m$-widely acceptable sequence under sub-linear expectations",
  "authors": [
    "Mingzhou Xu",
    "Xuhang Kong"
  ],
  "comment": "16 pages,submitted to Journal of Inequalities and Applications",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, the complete moment convergence for the partial sum of moving average processes $\\{X_n=\\sum_{i=-\\infty}^{\\infty}a_iY_{i+n},n\\ge 1\\}$ is estabished under some proper conditions, where $\\{Y_i,-\\infty<i<\\infty\\}$ is a sequence of $m$-widely acceptable ($m$-WA) random variables, which is stochastically dominated by a random variable $Y$ in sub-linear expectations space $(\\Omega,\\HH,\\ee)$ and $\\{a_i,-\\infty<i<\\infty\\}$ is an absolutely summable sequence of real numbers. The results extend the relevant results in probability space to those under sub-linear expectations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-27T06:59:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F15",
      "60F05"
    ],
    "keywords": [
      "complete moment convergence",
      "moving average processes",
      "acceptable sequence",
      "sub-linear expectations space",
      "results extend"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}