{
  "id": "0805.1949",
  "version": "v1",
  "published": "2008-05-13T22:31:15.000Z",
  "updated": "2008-05-13T22:31:15.000Z",
  "title": "Aggregation of weakly dependent doubly stochastic processes",
  "authors": [
    "Lisandro J. Fermin"
  ],
  "comment": "33 pages",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "The aim of this paper is to extend the aggregation convergence results given in (Dacunha-Castelle and Fermin 2005, Dacunha-Castelle and Fermin 2008) to doubly stochastic linear and nonlinear processes with weakly dependent innovations. First, we introduce a weak dependence notion for doubly stochastic processes, based in the weak dependence definition given in (Doukhan and Louhichi 1999), and we exhibe several models satisfying this notion, such as: doubly stochastic Volterra processes and doubly stochastic Bernoulli scheme with weakly dependent innovations. Afterwards we derive a central limit theorem for the partial aggregation sequence considering weakly dependent doubly stochastic processes. Finally, show a new SLLN for the covariance function of the partial aggregation process in the case of doubly stochastic Volterra processes with interactive innovations. Keywords: Aggregation, weak dependence, doubly stochastic processes, Volterra processes, Bernoulli shift, TCL, SLLN.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-13T22:31:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G10",
      "60F05",
      "60F15"
    ],
    "keywords": [
      "weakly dependent doubly stochastic processes",
      "aggregation",
      "doubly stochastic volterra processes",
      "weak dependence",
      "sequence considering weakly dependent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.1949F"
    }
  }
}