{
  "id": "0807.3268",
  "version": "v1",
  "published": "2008-07-21T14:05:38.000Z",
  "updated": "2008-07-21T14:05:38.000Z",
  "title": "Convergence of symmetric Markov chains on $\\Z^d$",
  "authors": [
    "R. F. Bass",
    "T. Kumagai",
    "T. Uemura"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "For each $n$ let $Y^n_t$ be a continuous time symmetric Markov chain with state space $n^{-1} \\Z^d$. A condition in terms of the conductances is given for the convergence of the $Y^n_t$ to a symmetric Markov process $Y_t$ on $\\R^d$. We have weak convergence of $\\{Y^n_t: t\\leq t_0\\}$ for every $t_0$ and every starting point. The limit process $Y$ has a continuous part and may also have jumps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-07-21T14:05:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10"
    ],
    "keywords": [
      "continuous time symmetric markov chain",
      "symmetric markov process",
      "state space",
      "weak convergence",
      "limit process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.3268B"
    }
  }
}