{
  "id": "1310.7770",
  "version": "v1",
  "published": "2013-10-29T12:00:46.000Z",
  "updated": "2013-10-29T12:00:46.000Z",
  "title": "Moment asymptotics for multitype branching random walks in random environment",
  "authors": [
    "Onur Gün",
    "Wolfgang König",
    "Ozren Sekulović"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a discrete time multitype branching random walk on a finite space with finite set of types. Particles follow a Markov chain on the spatial space whereas offspring distributions are given by a random field that is fixed throughout the evolution of the particles. Our main interest lies in the averaged (annealed) expectation of the population size, and its long-time asymptotics. We first derive, for fixed time, a formula for the expected population size with fixed offspring distributions, which is reminiscent of a Feynman-Kac formula. We choose Weibull-type distributions with parameter $1/\\rho_{ij}$ for the upper tail of the mean number of $j$ type particles produced by an $i$ type particle. We derive the first two terms of the long-time asymptotics, which are written as two coupled variational formulas, and interpret them in terms of the typical behavior of the system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-29T12:00:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60J55",
      "60F10",
      "60K37",
      "60J10"
    ],
    "keywords": [
      "moment asymptotics",
      "random environment",
      "time multitype branching random walk",
      "discrete time multitype branching random",
      "long-time asymptotics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.7770G"
    }
  }
}