{
  "id": "2101.09045",
  "version": "v1",
  "published": "2021-01-22T10:36:49.000Z",
  "updated": "2021-01-22T10:36:49.000Z",
  "title": "Inference of Markov models from trajectories via Large Deviations at Level 2.5 with applications to Random Walks in Random Media",
  "authors": [
    "Cecile Monthus"
  ],
  "comment": "23 pages",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "The inference of Markov models from data on stochastic dynamical trajectories over the time-window $T$ is revisited via the large deviations at Level 2.5 for the time-empirical density and the time-empirical flows in order to obtain the large deviations properties of the inferred Markov parameters for large $T$. The explicit rate functions are given for several settings, namely discrete-time Markov chains, continuous-time Markov jump processes, and diffusion processes in dimension $d$. Applications to various models of random walks in random media are described, where the goal is to infer the quenched random variables defining a given disordered sample.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-22T10:36:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random walks",
      "markov models",
      "random media",
      "applications",
      "trajectories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}