{
  "id": "1704.05530",
  "version": "v1",
  "published": "2017-04-15T21:51:47.000Z",
  "updated": "2017-04-15T21:51:47.000Z",
  "title": "Nonstandard Martingales, Markov Chains and the Heat Equation",
  "authors": [
    "Tristram de Piro"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We construct a nonstandard martingale from a discrete Markov chain. This is shown to be useful for solving the heat equation with a non smooth initial condition. We show that the nonstandard solution to the heat equation with a smooth initial condition specialises to the classical solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-15T21:51:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heat equation",
      "nonstandard martingale",
      "smooth initial condition specialises",
      "non smooth initial condition",
      "discrete markov chain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}