{
  "id": "1907.06812",
  "version": "v1",
  "published": "2019-07-16T02:37:59.000Z",
  "updated": "2019-07-16T02:37:59.000Z",
  "title": "Stochastic viscosity solutions for stochastic integral-partial differential equations and singular stochastic control",
  "authors": [
    "Jinbiao Wu"
  ],
  "comment": "47 pages",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "In this article, we mainly study stochastic viscosity solutions for a class of semilinear stochastic integral-partial differential equations (SIPDEs). We investigate a new class of generalized backward doubly stochastic differential equations (GBDSDEs) driven by two independent Brownian motions and an independent Poisson random measure, which involves an integral with respect to a c\\`{a}dl\\`{a}g increasing process. We first derive existence and uniqueness of the solution of GBDSDEs with general jumps. We then introduce the definition of stochastic viscosity solutions of SIPDEs and give a probabilistic representation for stochastic viscosity solutions of semilinear SIPDEs with nonlinear Neumann boundary conditions. Finally, we establish stochastic maximum principles for the optimal control of a stochastic system modelled by a GBDSDE with general jumps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-16T02:37:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H10",
      "93E20"
    ],
    "keywords": [
      "stochastic viscosity solutions",
      "singular stochastic control",
      "doubly stochastic differential equations",
      "backward doubly stochastic differential",
      "semilinear stochastic integral-partial differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}