{
  "id": "1703.07234",
  "version": "v1",
  "published": "2017-03-21T14:23:30.000Z",
  "updated": "2017-03-21T14:23:30.000Z",
  "title": "Convergence of Brownian Motions on Metric Measure Spaces Under Riemannian Curvature-Dimension Conditions",
  "authors": [
    "Kohei Suzuki"
  ],
  "comment": "39 pages, 3 figures. The previous two manuscripts arXiv:1509.02025 and arXiv:1603.08622 are combined in this preprint",
  "categories": [
    "math.PR",
    "math.MG"
  ],
  "abstract": "We show that the pointed measured Gromov convergence of the underlying spaces implies (or under some condition, is equivalent to) the weak convergence of Brownian motions under Riemannian Curvature-Dimension (RCD) conditions. This paper is an improved and jointed version of the previous two manuscripts arXiv:1509.02025 and arXiv:1603.08622. The improvements extend our results to the case of sigma-finite reference measures and to the case that initial distributions of Brownian motions are possible to be dirac measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-21T14:23:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F17",
      "53C23"
    ],
    "keywords": [
      "brownian motions",
      "metric measure spaces",
      "riemannian curvature-dimension conditions",
      "sigma-finite reference measures",
      "measured gromov convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}