{
  "id": "0709.3713",
  "version": "v2",
  "published": "2007-09-24T08:57:34.000Z",
  "updated": "2009-03-06T13:25:54.000Z",
  "title": "Existence, uniqueness and approximation for stochastic Schrodinger equation: the Poisson case",
  "authors": [
    "Clement Pellegrini"
  ],
  "comment": "35 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "In quantum physics, recent investigations deal with the so-called \"quantum trajectory\" theory. Heuristic rules are usually used to give rise to \"stochastic Schrodinger equations\" which are stochastic differential equations of non-usual type describing the physical models. These equations pose tedious problems in terms of mathematical justification: notion of solution, existence, uniqueness, justification... In this article, we concentrate on a particular case: the Poisson case. Random measure theory is used in order to give rigorous sense to such equations. We prove existence and uniqueness of a solution for the associated stochastic equation. Furthermore, the stochastic model is physically justified by proving that the solution can be obtained as a limit of a concrete discrete time physical model.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-06T13:25:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic schrodinger equation",
      "poisson case",
      "uniqueness",
      "approximation",
      "concrete discrete time physical model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.3713P"
    }
  }
}