{
  "id": "1707.01019",
  "version": "v1",
  "published": "2017-07-04T14:41:21.000Z",
  "updated": "2017-07-04T14:41:21.000Z",
  "title": "Mixingales on Riesz spaces",
  "authors": [
    "Wen-Chi Kuo",
    "Jessica Joy Vardy",
    "Bruce Alastair Watson"
  ],
  "journal": "Journal of Mathematical Analysis and Applications, 402 (2013), 731-738",
  "doi": "10.1016/j.jmaa.2013.02.001",
  "categories": [
    "math.PR",
    "math.FA",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "A mixingale is a stochastic process which combines properties of martingales and mixing sequences. McLeish introduced the term mixingale at the $4^{th}$ Conference on Stochastic Processes and Application, at York University, Toronto, 1974, in the context of $L^2$. In this paper we generalize the concept of a mixingale to the measure-free Riesz space setting (this generalizes all of the $L^p, 1\\le p\\le \\infty$ variants) and prove that a weak law of large numbers holds for Riesz space mixingales. In the process we also generalize the concept of uniform integrability to the Riesz space setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-04T14:41:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B60",
      "60G42",
      "60G20",
      "46G40"
    ],
    "keywords": [
      "stochastic process",
      "riesz space mixingales",
      "large numbers holds",
      "term mixingale",
      "weak law"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}