{
  "id": "1910.03946",
  "version": "v1",
  "published": "2019-10-09T12:29:51.000Z",
  "updated": "2019-10-09T12:29:51.000Z",
  "title": "The exponential resolvent of a Markov process and large deviations for Markov processes via Hamilton-Jacobi equations",
  "authors": [
    "Richard C. Kraaij"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the Hamilton-Jacobi equation f - lambda Hf = h, where H f = e^{-f}Ae^f and where A is an operator that corresponds to a well-posed martingale problem. We identify an operator that gives viscosity solutions to the Hamilton-Jacobi equation, and which can therefore be interpreted as the resolvent of H. The operator is given in terms of optimization problem where the running cost is a path-space relative entropy. Finally, we use the resolvents to give a new proof of the abstract large deviation result of Feng and Kurtz.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-09T12:29:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "markov process",
      "hamilton-jacobi equation",
      "exponential resolvent",
      "abstract large deviation result",
      "well-posed martingale problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}