{
  "id": "0707.4546",
  "version": "v1",
  "published": "2007-07-31T07:09:39.000Z",
  "updated": "2007-07-31T07:09:39.000Z",
  "title": "Good rough path sequences and applications to anticipating stochastic calculus",
  "authors": [
    "Laure Coutin",
    "Peter Friz",
    "Nicolas Victoir"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009117906000000827 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2007, Vol. 35, No. 3, 1172-1193",
  "doi": "10.1214/009117906000000827",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process lifted to a rough path. Neither adaptedness of initial point and vector fields nor commuting conditions between vector field is assumed. Under a simple condition on the stochastic process, we show that the unique solution of the above SDE understood in the rough path sense is actually a Stratonovich solution. We then show that this condition is satisfied by the Brownian motion. As application, we obtain rather flexible results such as support theorems, large deviation principles and Wong--Zakai approximations for SDEs driven by Brownian motion along anticipating vectorfields. In particular, this unifies many results on anticipative SDEs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-31T07:09:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H99"
    ],
    "keywords": [
      "rough path sequences",
      "anticipating stochastic calculus",
      "stratonovich stochastic differential equations driven",
      "application",
      "anticipative stratonovich stochastic differential equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.4546C"
    }
  }
}