{
  "id": "2010.05292",
  "version": "v1",
  "published": "2020-10-11T17:38:34.000Z",
  "updated": "2020-10-11T17:38:34.000Z",
  "title": "Stochastic integration with respect to cylindrical semimartingales",
  "authors": [
    "C. A. Fonseca-Mora"
  ],
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "In this work we introduce a theory of stochastic integration with respect to general cylindrical semimartingales in the dual $\\Phi'$ of a locally convex space $\\Phi$. Our construction of the stochastic integral is based on the theory of tensor products of topological vector spaces and the property of good integrators of real-valued semimartingales. This theory is further developed in the case where $\\Phi$ is a complete, barrelled, nuclear space, where we obtain a complete description of the class of integrands as $\\Phi$-valued locally bounded and weakly predictable processes. Several other properties of the stochastic integral are proven, including a Riemann representation and a integration by parts formula. Finally, as an application to our theory we define stochastic integrals with respect to a sequence of real-valued semimartingales.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-11T17:38:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H05",
      "60B11",
      "60G20",
      "60G48"
    ],
    "keywords": [
      "stochastic integration",
      "real-valued semimartingales",
      "define stochastic integrals",
      "locally convex space",
      "complete description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}