{
  "id": "2406.07881",
  "version": "v1",
  "published": "2024-06-12T05:20:01.000Z",
  "updated": "2024-06-12T05:20:01.000Z",
  "title": "McKean-Vlasov Forward-backward doubly stochastic differential equations and applications to stochastic control",
  "authors": [
    "AbdulRahman Al-Hussein",
    "Abdelhakim Ninouh",
    "Boulakhras Gherbal"
  ],
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "This paper investigates first the existence and uniqueness of solutions for McKean-Vlasov forward-backward doubly stochastic differential equations (MV-FBDSDEs) in infinite-dimensional real separable Hilbert spaces. These equations combine the features of forward-backward doubly stochastic differential equations with the mean-field approach, allowing the coefficients to depend on the solution distribution. We establish the existence and uniqueness of solutions for MV-FBDSDEs using the method of continuation and provide an example and a counterexample to illustrate our findings. Moreover, we extend the practical applicability of our results by employing them within the context of the stochastic maximum principle for a control problem governed by MV-FBDSDEs. This study contributes to the field of stochastic control problems and presents the first analysis of MV-FBDSDEs in infinite-dimensional spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-12T05:20:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "93E20"
    ],
    "keywords": [
      "forward-backward doubly stochastic differential equations",
      "mckean-vlasov forward-backward doubly stochastic differential",
      "stochastic control",
      "real separable hilbert spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}