{
  "id": "1903.05045",
  "version": "v1",
  "published": "2019-03-12T16:52:50.000Z",
  "updated": "2019-03-12T16:52:50.000Z",
  "title": "Stochastic Volterra integral equations and a class of first order stochastic partial differential equations",
  "authors": [
    "Fred Espen Benth",
    "Nils Detering",
    "Paul Kruehner"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We investigate stochastic Volterra equations and their limiting laws. The stochastic Volterra equations we consider are driven by a Hilbert space valued \\Levy noise and integration kernels may have non-linear dependence on the current state of the process. Our method is based on an embedding into a Hilbert space of functions which allows to represent the solution of the Volterra equation as the boundary value of a solution to a stochastic partial differential equation. We first gather abstract results and give more detailed conditions in more specific function spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-12T16:52:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60Hxx",
      "60H15",
      "60H20"
    ],
    "keywords": [
      "order stochastic partial differential equations",
      "first order stochastic partial differential",
      "stochastic volterra integral equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}