{
  "id": "1901.08478",
  "version": "v1",
  "published": "2019-01-24T16:12:30.000Z",
  "updated": "2019-01-24T16:12:30.000Z",
  "title": "Large-deviation principles of switching Markov processes via Hamilton-Jacobi equations",
  "authors": [
    "Mark A. Peletier",
    "Mikola C. Schlottke"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove path-space large-deviation principles of switching Markov processes by exploiting the connection to associated Hamilton-Jacobi equations, following Jin Feng's and Thomas Kurtz's method. In the limit that we consider, we show how the large-deviation problem in path-space essentially reduces to a spectral problem of finding principal eigenvalues. The large-deviation rate functions are given in action-integral form. As an application, we demonstrate how macroscopic transport properties of both continuous and discrete microscopic models of molecular-motor systems can be deduced from an associated principal-eigenvalue problem. The precise characterization of the macroscopic velocity in terms of principal eigenvalues implies that breaking of detailed balance is necessary for obtaining transport. In this way, we extend and generalize existing results about molecular motors and explicitly place them in the framework of stochastic processes and large-deviation principles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-24T16:12:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60G51",
      "60J25",
      "35F21",
      "82C41",
      "92C10"
    ],
    "keywords": [
      "switching markov processes",
      "hamilton-jacobi equations",
      "path-space large-deviation principles",
      "principal eigenvalues implies",
      "discrete microscopic models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}