{
  "id": "1008.2682",
  "version": "v1",
  "published": "2010-08-16T15:11:01.000Z",
  "updated": "2010-08-16T15:11:01.000Z",
  "title": "On the Existence Theory of Hilbert Space valued Diffusion Processes",
  "authors": [
    "Günter Hinrichs"
  ],
  "comment": "43 pages, Diploma thesis",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that the solution of certain linear stochastic differential equations in Hilbert spaces, namely those with bounded operators as well as the conservative stochastic Schr\\\"odinger equations, can be obtained - along the lines of the Lie-Trotter product formula from semigroup theory - by splitting the equation into a ``deterministic'' and a ``stochastic'' part and alternately applying the corresponding solution flows in an iterative manner to the initial value.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-16T15:11:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15"
    ],
    "keywords": [
      "hilbert space valued diffusion processes",
      "existence theory",
      "linear stochastic differential equations",
      "lie-trotter product formula",
      "initial value"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.2682H"
    }
  }
}