{
  "id": "1502.05648",
  "version": "v1",
  "published": "2015-02-19T17:46:19.000Z",
  "updated": "2015-02-19T17:46:19.000Z",
  "title": "Path-dependent equations and viscosity solutions in infinite dimension",
  "authors": [
    "Andrea Cosso",
    "Salvatore Federico",
    "Fausto Gozzi",
    "Mauro Rosestolato",
    "Nizar Touzi"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Path Dependent PDE's (PPDE's) are natural objects to study when one deals with non Markovian models. Recently, after the introduction (see [12]) of the so-called pathwise (or functional or Dupire) calculus, various papers have been devoted to study the well-posedness of such kind of equations, both from the point of view of regular solutions (see e.g. [18]) and viscosity solutions (see e.g. [13]), in the case of finite dimensional underlying space. In this paper, motivated by the study of models driven by path dependent stochastic PDE's, we give a first well-posedness result for viscosity solutions of PPDE's when the underlying space is an infinite dimensional Hilbert space. The proof requires a substantial modification of the approach followed in the finite dimensional case. We also observe that, differently from the finite dimensional case, our well-posedness result, even in the Markovian case, apply to equations which cannot be treated, up to now, with the known theory of viscosity solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-19T17:46:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "viscosity solutions",
      "path-dependent equations",
      "finite dimensional case",
      "infinite dimensional hilbert space",
      "well-posedness result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}