{
  "id": "0902.4195",
  "version": "v1",
  "published": "2009-02-24T17:09:04.000Z",
  "updated": "2009-02-24T17:09:04.000Z",
  "title": "Stationarity, time--reversal and fluctuation theory for a class of piecewise deterministic Markov processes",
  "authors": [
    "Alessandra Faggionato",
    "Davide Gabrielli",
    "Marco Ribezzi Crivellari"
  ],
  "comment": "45 pages",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \\s)\\in \\O\\times \\G$, $\\O$ being a region in $\\bbR^d$ or the $d$--dimensional torus, $\\G$ being a finite set. The continuous variable $x$ follows a piecewise deterministic dynamics, the discrete variable $\\s$ evolves by a stochastic jump dynamics and the two resulting evolutions are fully--coupled. We study stationarity, reversibility and time--reversal symmetries of the process. Increasing the frequency of the $\\s$--jumps, we show that the system behaves asymptotically as deterministic and we investigate the structure of fluctuations (i.e. deviations from the asymptotic behavior), recovering in a non Markovian frame results obtained by Bertini et al. \\cite{BDGJL1, BDGJL2, BDGJL3, BDGJL4}, in the context of Markovian stochastic interacting particle systems. Finally, we discuss a Gallavotti--Cohen--type symmetry relation with involution map different from time--reversal. For several examples the above results are recovered by explicit computations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-24T17:09:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "piecewise deterministic markov processes",
      "fluctuation theory",
      "time-reversal",
      "stationarity",
      "markovian stochastic interacting particle systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.4195F"
    }
  }
}