{
  "id": "1505.06772",
  "version": "v1",
  "published": "2015-05-25T22:23:06.000Z",
  "updated": "2015-05-25T22:23:06.000Z",
  "title": "Stochastic Homogenisation On Homogeneous Spaces",
  "authors": [
    "Xue-Mei Li"
  ],
  "comment": "41 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let G be a Lie group with a closed subgroup H and a left invariant Riemannian metric. We study a family of stochastic differential equations arising from inhomogeneous scaling of the Riemannian metric. Such equations interpolate between horizontal exponential maps on G and diffusions on H. Suppose that the homogeneous space has a reductive decomposition and the horizontal direction is not invariant under the adjoint action of H. We obtain a pair of effective stochastic processes on G and on the homogeneous manifold M respectively and we classify their limits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-25T22:23:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homogeneous space",
      "stochastic homogenisation",
      "left invariant riemannian metric",
      "horizontal exponential maps",
      "lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150506772L"
    }
  }
}