{
  "id": "2005.01232",
  "version": "v1",
  "published": "2020-05-04T01:43:16.000Z",
  "updated": "2020-05-04T01:43:16.000Z",
  "title": "Controlled Ordinary Differential Equations with Random Path-Dependent Coefficients and Stochastic Path-Dependent Hamilton-Jacobi Equations",
  "authors": [
    "Jinniao Qiu"
  ],
  "comment": "22 pages",
  "categories": [
    "math.OC",
    "math.PR"
  ],
  "abstract": "This paper is devoted to the stochastic optimal control problem of ordinary differential equations allowing for both path-dependent and random coefficients. As opposed to the {deterministic} path-dependent cases, the value function turns out to be a random field on the path spaces and it is characterized with a stochastic path-dependent Hamilton-Jacobi (SPHJ) equation. A notion of viscosity solution is proposed and the value function is proved to be the unique viscosity solution to the associated SPHJ equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-04T01:43:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic path-dependent hamilton-jacobi equations",
      "controlled ordinary differential equations",
      "random path-dependent coefficients",
      "stochastic optimal control problem",
      "viscosity solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}