{
  "id": "2311.15205",
  "version": "v1",
  "published": "2023-11-26T06:08:33.000Z",
  "updated": "2023-11-26T06:08:33.000Z",
  "title": "Discrete stopping times in the lattice of continuous functions",
  "authors": [
    "Achintya Raya Polavarapu"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "A functional calculus for an order complete vector lattice $\\mathcal{E}$ was developed by Grobler in 2014 using the Daniell integral. We show that if one represents the universal completion of $\\mathcal{E}$ as $C^\\infty(K)$, then the Daniell functional calculus for continuous functions is exactly the pointwise composition of functions in $C^\\infty(K)$. This representation allows an easy deduction of the various properties of the functional calculus. Afterwards, we study discrete stopping times and stopped processes in $C^\\infty(K)$. We obtain a representation that is analogous to what is expected in probability theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-26T06:08:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46A40",
      "46E05",
      "60G20",
      "60G40"
    ],
    "keywords": [
      "continuous functions",
      "order complete vector lattice",
      "daniell functional calculus",
      "study discrete stopping times",
      "representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}