{
  "id": "1701.02905",
  "version": "v1",
  "published": "2017-01-11T09:49:38.000Z",
  "updated": "2017-01-11T09:49:38.000Z",
  "title": "On semi-Markov processes and their Kolmogorov's integro-differential equations",
  "authors": [
    "Enzo Orsingher",
    "Costantino Ricciuti",
    "Bruno Toaldo"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Semi-Markov processes are a generalization of Markov processes since the exponential distribution of time intervals is replaced with an arbitrary distribution. This paper provides an integro-differential form of the Kolmogorov's backward equations for a large class of homogeneous semi-Markov processes, having the form of a Volterra integro-differential equation. An equivalent evolutionary (differential) form of the equations is also provided. Weak limits of semi-Markov processes are also considered and their corresponding integro-differential Kolmogorov's equations are identified.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-11T09:49:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K15",
      "60J25",
      "60G51"
    ],
    "keywords": [
      "semi-markov processes",
      "kolmogorovs integro-differential equations",
      "corresponding integro-differential kolmogorovs equations",
      "volterra integro-differential equation",
      "time intervals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}