{
  "id": "1304.5169",
  "version": "v2",
  "published": "2013-04-18T15:58:28.000Z",
  "updated": "2015-01-30T20:01:35.000Z",
  "title": "Moment growth bounds on continuous time Markov processes on non-negative integer lattices",
  "authors": [
    "Muruhan Rathinam"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider Markov processes in continuous time with state space $\\posint^N$ and provide two sufficient conditions and one necessary condition for the existence of moments $E(\\|X(t)\\|^r)$ of all orders $r \\in \\nat$ for all $t \\geq 0$. The sufficient conditions also guarantee an exponential in time growth bound for the moments. The class of processes studied have finitely many state independent jumpsize vectors $\\nu_1,\\dots,\\nu_M$. This class of processes arise naturally in many applications such as stochastic models of chemical kinetics, population dynamics and queueing theory for example. We also provide a necessary and sufficient condition for stochiometric boundedness of species in terms of $\\nu_j$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-18T15:58:28.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-30T20:01:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous time markov processes",
      "moment growth bounds",
      "non-negative integer lattices",
      "sufficient condition",
      "time growth bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.5169R"
    }
  }
}