{
  "id": "1508.06147",
  "version": "v1",
  "published": "2015-08-25T13:37:20.000Z",
  "updated": "2015-08-25T13:37:20.000Z",
  "title": "On distributions of diffusion processes in Hilbert spaces at a fixed moment in time",
  "authors": [
    "Oxana Manita"
  ],
  "comment": "12 pages",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We consider diffusion processes in Hilbert space, corresponding to stochastic partial differential equations. We show that a non-degenerate diffusion process at any moment in time is situated in any given ellipsoid, the parameters of which are adjusted to the Wiener process, with a strictly positive probability. This is a partial infinite-dimensional analogue of the existence of a positive density (with respect to the Lebesgue measure) of the transition probability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-25T13:37:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G07",
      "35K90",
      "35K15",
      "35B09"
    ],
    "keywords": [
      "hilbert space",
      "fixed moment",
      "distributions",
      "stochastic partial differential equations",
      "partial infinite-dimensional analogue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150806147M"
    }
  }
}