{
  "id": "1706.07978",
  "version": "v1",
  "published": "2017-06-24T16:18:37.000Z",
  "updated": "2017-06-24T16:18:37.000Z",
  "title": "Martingale-coboundary decomposition for stationary random fields",
  "authors": [
    "Dalibor Volny"
  ],
  "comment": "Stochastics and Dynamics 2017",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove a martingale-coboundary representation for random fields with a completely commuting filtration. For random variables in L2 we present a necessary and sufficient condition which is a generalization of Heyde's condition for one dimensional processes from 1975. For Lp spaces with 2 \\leq p < \\infty we give a necessary and sufficient condition which extends Volny's result from 1993 to random fields and improves condition of El Machkouri and Giraudo from 2016 (arXiv:1410.3062). In application, new weak invariance principle and estimates of large deviations are found.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-24T16:18:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G60",
      "60G42",
      "60F17"
    ],
    "keywords": [
      "stationary random fields",
      "martingale-coboundary decomposition",
      "sufficient condition",
      "extends volnys result",
      "weak invariance principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}