{
  "id": "1707.07828",
  "version": "v1",
  "published": "2017-07-25T06:25:18.000Z",
  "updated": "2017-07-25T06:25:18.000Z",
  "title": "On the path-independence of the Girsanov transformation for stochastic evolution equations with jumps in Hilbert spaces",
  "authors": [
    "Huijie Qiao",
    "Jianglun Wu"
  ],
  "comment": "21 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Based on a recent result on characterising the path-independence of the Girsanov transformation for non-Lipschnitz stochastic differential equations (SDEs) with jumps on $R^d$, in this paper, we extend our consideration of characterising the path-indpendent property from finite-dimensional SDEs with jumps to stochastic evolution equations with jumps in Hilbert spaces. This is done via Galerkin type finite-dimensional approximations of the infinite-dimensional stochastic evolution equations with jumps in the manner that one could then link the characterisation of the path-independence for finite-dimensional jump type SDEs to that for the infinite-dimensional settings. Our result provides an intrinsic link of infinite-dimensional stochastic evolution equations with jumps to infinite-dimensional partial integro-differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-25T06:25:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H30",
      "35R60"
    ],
    "keywords": [
      "girsanov transformation",
      "hilbert spaces",
      "infinite-dimensional stochastic evolution equations",
      "path-independence",
      "non-lipschnitz stochastic differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}