{
  "id": "1405.5822",
  "version": "v2",
  "published": "2014-05-22T16:39:38.000Z",
  "updated": "2014-10-13T16:47:20.000Z",
  "title": "Backward Doubly SDEs and Semilinear Stochastic PDEs in a convex domain",
  "authors": [
    "Matoussi Anis",
    "Sabbagh Wissal"
  ],
  "comment": "This paper has been withdrawn by the author due to a crucial sign error in the proof of some Lemma",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper presents existence and uniqueness results for reflected backward doubly stochastic differential equations (in short RBDDSEs) in a convex domain D without any regularity conditions on the boundary. Moreover, using a stochastic flow approach a probabilistic interpretation for a class of reflected SPDE's in a domain is given via such RBDSDEs. The solution is expressed as a pair (u,{\\nu}) where u is a predictable continuous process which takes values in a Sobolev space and {\\nu} is a random regular measure. The bounded variation process K, component of the solution of the reflected BDSDE, controls the set when u reaches the boundary of D. This bounded variation process determines the measure m from a particular relation by using the inverse of the flow associated to the the diffusion operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-22T16:39:38.000Z",
      "comment": "26. arXiv admin note: text overlap with arXiv:1307.0875",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-13T16:47:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60G46",
      "35H60"
    ],
    "keywords": [
      "semilinear stochastic pdes",
      "convex domain",
      "backward doubly sdes",
      "doubly stochastic differential equations",
      "backward doubly stochastic differential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.5822A"
    }
  }
}