{
  "id": "2201.08196",
  "version": "v1",
  "published": "2022-01-20T14:21:54.000Z",
  "updated": "2022-01-20T14:21:54.000Z",
  "title": "The wave speed of an FKPP equation with jumps via coordinated branching",
  "authors": [
    "Tommaso Rosati",
    "András Tóbiás"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a Fisher-KPP equation with nonlinear selection driven by a Poisson random measure. We prove that the equation admits a unique wave speed $ \\mathfrak{s}> 0 $ given by $\\frac{\\mathfrak{s}^{2}}{2} = \\int_{[0, 1]}\\frac{ \\log{(1 + y)}}{y} \\mathfrak{R}( \\mathrm d y)$ where $ \\mathfrak{R} $ is the intensity of the impacts of the driving noise. Our arguments are based on upper and lower bounds via a quenched duality with a coordinated system of branching Brownian motions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-20T14:21:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60J80",
      "35C07",
      "92D25"
    ],
    "keywords": [
      "fkpp equation",
      "coordinated branching",
      "nonlinear selection driven",
      "poisson random measure",
      "branching brownian motions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}