{
  "id": "2110.00750",
  "version": "v2",
  "published": "2021-10-02T08:11:36.000Z",
  "updated": "2025-01-03T09:12:58.000Z",
  "title": "Probabilistic representation of parabolic stochastic variational inequality with Dirichlet-Neumann boundary and variational generalized backward doubly stochastic differential equations",
  "authors": [
    "Yong Ren",
    "Auguste Aman",
    "Qing Zhou"
  ],
  "comment": "This version is 39 pages long and has been accepted to Stochastics who will publish the final version",
  "doi": "10.1080/17442508.2025.2449646",
  "categories": [
    "math.PR"
  ],
  "abstract": "We derive the existence and uniqueness of the generalized backward doubly stochastic differential equation with sub-differential of a lower semi-continuous convex function under a non Lipschitz condition. This study allows us give a probabilistic representation (in stochastic viscosity sense) to the parabolic variational stochastic partial differential equations with Dirichlet-Neumann conditions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-01-03T09:12:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H20"
    ],
    "keywords": [
      "backward doubly stochastic differential equation",
      "generalized backward doubly stochastic differential",
      "variational generalized backward doubly stochastic",
      "parabolic stochastic variational inequality",
      "probabilistic representation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Taylor-Francis"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}