{
  "id": "1307.3455",
  "version": "v1",
  "published": "2013-07-12T13:38:45.000Z",
  "updated": "2013-07-12T13:38:45.000Z",
  "title": "A comparison theorem for stochastic differential equations under a Novikov-type condition",
  "authors": [
    "Alberto Lanconelli"
  ],
  "comment": "13 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a system of stochastic differential equations driven by a standard n-dimensional Brownian motion where the drift coefficient satisfies a Novikov-type condition while the diffusion coefficient is the identity matrix. We define a vector Z of square integrable stochastic processes with the following property: if the filtration of the translated Brownian motion obtained from the Girsanov transform coincides with the one of the driving noise then Z coincides with the unique strong solution of the equation; otherwise the process Z solves in the strong sense a related stochastic differential inequality. This fact together with an additional assumption will provide a comparison result similar to well known theorems obtained in the presence of strong solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-12T13:38:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10"
    ],
    "keywords": [
      "novikov-type condition",
      "comparison theorem",
      "standard n-dimensional brownian motion",
      "stochastic differential equations driven",
      "comparison result similar"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.3455L"
    }
  }
}