{
  "id": "1710.09263",
  "version": "v1",
  "published": "2017-10-25T14:36:34.000Z",
  "updated": "2017-10-25T14:36:34.000Z",
  "title": "Multivariate functional approximations with Stein's method of exchangeable pairs",
  "authors": [
    "Mikolaj J. Kasprzak"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We combine the multivariate method of exchangeable pairs with Stein's method for functional approximation and give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply this approach to estimate the distance from a pre-limiting mixture process of a sum of random variables chosen from an array according to a random permutation and prove a functional combinatorial central limit theorem. We also consider a graph-valued process and bound the speed of convergence of the joint distribution of its rescaled edge and two-star counts to a two-dimensional continuous Gaussian process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-25T14:36:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B10",
      "60F17",
      "60B12",
      "60J65",
      "60E05",
      "60E15"
    ],
    "keywords": [
      "multivariate functional approximations",
      "steins method",
      "exchangeable pairs",
      "functional combinatorial central limit theorem",
      "abstract gaussian approximation theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}