{
  "id": "1803.04525",
  "version": "v1",
  "published": "2018-03-12T20:51:32.000Z",
  "updated": "2018-03-12T20:51:32.000Z",
  "title": "Well-posedness of Hamilton-Jacobi equations in population dynamics and applications to large deviations",
  "authors": [
    "Richard C. Kraaij",
    "Louis Mahé"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove Freidlin-Wentzell type large deviation principles for various rescaled models in populations dynamics that have immigration and possibly harvesting: birth-death processes, Galton-Watson trees, epidemic SI models, and prey-predator models. The proofs are carried out using a general analytic approach based on the well-posedness of a class of associated Hamilton-Jacobi equations. The notable feature for these Hamilton-Jacobi equations is that the Hamiltonian can be discontinuous at the boundary. We prove a well-posedness result for a large class of Hamilton-Jacobi equations corresponding to one-dimensional models, and give partial results for the multi-dimensional setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-12T20:51:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49L25",
      "60F10",
      "60J80",
      "92D25"
    ],
    "keywords": [
      "hamilton-jacobi equations",
      "population dynamics",
      "well-posedness",
      "freidlin-wentzell type large deviation principles",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}