{
  "id": "2305.17276",
  "version": "v1",
  "published": "2023-05-26T21:45:57.000Z",
  "updated": "2023-05-26T21:45:57.000Z",
  "title": "Differentiability of the effective Lagrangian for Hamilton-Jacobi-Bellman equations in dynamic random environments",
  "authors": [
    "Yuri Bakhtin",
    "Douglas Dow"
  ],
  "comment": "27 pages",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We prove differentiability of the effective Lagrangian for continuous time multidimensional directed variational problems in random dynamic environments with positive dependence range in time. This implies that limiting fundamental solutions in the associated homogenization problems for HJB equations are classical.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-26T21:45:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "82B44",
      "35B27",
      "49L12"
    ],
    "keywords": [
      "dynamic random environments",
      "effective lagrangian",
      "hamilton-jacobi-bellman equations",
      "differentiability",
      "time multidimensional directed variational problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}