{
  "id": "1904.12160",
  "version": "v1",
  "published": "2019-04-27T13:48:20.000Z",
  "updated": "2019-04-27T13:48:20.000Z",
  "title": "On the Feynman-Kac Formula",
  "authors": [
    "B Rajeev"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, given $y :[0,\\eta)\\rightarrow H$ a continuous map into a Hilbert space $H$ we study the equation \\[\\hat y(t) = e^{\\int_0^tc(s,\\hat y)}y(t)\\] where $c(s,\\cdot)$ is a given `potential' on $C([0,\\eta),H)$. Applying the transformation $y \\rightarrow \\hat y$ to the solutions of the SPDE and PDE underlying a diffusion, we study the Feynman-Kac formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-27T13:48:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60H10",
      "60H15"
    ],
    "keywords": [
      "feynman-kac formula",
      "hilbert space",
      "continuous map",
      "transformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}