{
  "id": "2112.07005",
  "version": "v2",
  "published": "2021-12-13T20:48:42.000Z",
  "updated": "2022-11-21T14:28:36.000Z",
  "title": "On the gap between deterministic and probabilistic Lyapunov exponents for continuous-time linear systems",
  "authors": [
    "Yacine Chitour",
    "Guilherme Mazanti",
    "Pierre Monmarché",
    "Mario Sigalotti"
  ],
  "categories": [
    "math.OC",
    "math.DS",
    "math.PR"
  ],
  "abstract": "Consider a non-autonomous continuous-time linear system in which the time-dependent matrix determining the dynamics is piecewise constant and takes finitely many values $A_1, \\dotsc, A_N$. This paper studies the equality cases between the maximal Lyapunov exponent associated with the set of matrices $\\{A_1, \\dotsc, A_N\\}$, on the one hand, and the corresponding ones for piecewise deterministic Markov processes with modes $A_1, \\dotsc, A_N$, on the other hand. A fundamental step in this study consists in establishing a result of independent interest, namely, that any sequence of Markov processes associated with the matrices $A_1,\\dotsc, A_N$ converges, up to extracting a subsequence, to a Markov process associated with a suitable convex combination of those matrices.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-11-21T14:28:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "34A38",
      "34D08"
    ],
    "keywords": [
      "probabilistic lyapunov exponents",
      "maximal lyapunov exponent",
      "non-autonomous continuous-time linear system",
      "piecewise deterministic markov processes",
      "study consists"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}