{
  "id": "0901.0623",
  "version": "v3",
  "published": "2009-01-06T10:47:44.000Z",
  "updated": "2011-06-07T20:33:12.000Z",
  "title": "Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence",
  "authors": [
    "Achim Klenke",
    "Leonid Mytnik"
  ],
  "comment": "35 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We construct a mutually catalytic branching process on a countable site space with infinite \"branching rate\". The finite rate mutually catalytic model, in which the rate of branching of one population at a site is proportional to the mass of the other population at that site, was introduced by Dawson and Perkins in [DP98]. We show that our model is the limit for a class of models and in particular for the Dawson-Perkins model as the rate of branching goes to infinity. Our process is characterized as the unique solution to a martingale problem. We also give a characterization of the process as a weak solution of an infinite system of stochastic integral equations driven by a Poisson noise.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-06-07T20:33:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37",
      "60J80",
      "60J65",
      "60J35"
    ],
    "keywords": [
      "infinite rate mutually catalytic branching",
      "characterization",
      "construction",
      "convergence",
      "stochastic integral equations driven"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0901.0623K"
    }
  }
}