{
  "id": "1504.01508",
  "version": "v1",
  "published": "2015-04-07T07:56:01.000Z",
  "updated": "2015-04-07T07:56:01.000Z",
  "title": "Stochastic averaging for multiscale Markov processes with an application to branching random walk in random environment",
  "authors": [
    "Martin Hutzenthaler",
    "Peter Pfaffelhuber"
  ],
  "comment": "18 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $Z = (Z_t)_{t\\in[0,\\infty)}$ be an ergodic Markov process and, for $n\\in\\mathbb{N}$, let $Z^n = (Z_{n^2 t})_{t\\in[0,\\infty)}$ drive a process $X^n$. Classical results show under suitable conditions that the sequence of non-Markovian processes $(X^n)_{n\\in\\mathbb{N}}$ converges to a Markov process and give its infinitesimal characteristics. Here, we consider a general sequence $(Z^n)_{n\\in\\mathbb{N}}$. Using a general result on stochastic averaging from [Kur92], we derive conditions which ensure that the sequence $(X^n)_{n\\in\\mathbb{N}}$ converges as in the classical case. As an application, we consider the diffusion limit of branching random walk in quickly evolving random environment.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-07T07:56:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05"
    ],
    "keywords": [
      "branching random walk",
      "multiscale markov processes",
      "stochastic averaging",
      "application",
      "ergodic markov process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150401508H"
    }
  }
}