{
  "id": "1602.06322",
  "version": "v1",
  "published": "2016-02-19T21:40:40.000Z",
  "updated": "2016-02-19T21:40:40.000Z",
  "title": "L^2-Perturbed Markov processes and applications to random walks in dynamic random environments",
  "authors": [
    "L. Avena",
    "O. Blondel",
    "A. Faggionato"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a Markov process satisfying a Poincar\\'e inequality w.r.t. a stationary, ergodic distribution $\\mu$ and perturb its generator by a bounded operator in $L^2(\\mu)$, thus leading to a new Markov process. By using a Dyson-Phillips type expansion, we prove that the perturbed Markov process has a unique invariant distribution absolutely continuous w.r.t. $\\mu$, which in addition is ergodic. We also derive a law of large numbers and an invariance principle for additive functionals for the perturbed Markov process. We apply these results to continuous-time random walks in dynamic random environments given by Markovian dynamics. Consequently, we prove a series expansion for the asymptotic speed of the random walk and an averaged invariance principle for its position. We provide a condition for non-degeneracy of the diffusion, and describe in some details equilibrium and convergence properties of the environment seen by the walker.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-19T21:40:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60F17",
      "82C22"
    ],
    "keywords": [
      "dynamic random environments",
      "perturbed markov process",
      "applications",
      "invariance principle",
      "dyson-phillips type expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160206322A"
    }
  }
}