{"ID":3083813,"CreatedAt":"2026-06-05T06:46:15.197025399Z","UpdatedAt":"2026-06-07T03:54:17.966829144Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.06018","arxiv_id":"2606.06018","title":"On statistical inference for non-linear dynamical systems evolving in their global attractor","abstract":"We consider a two-dimensional periodic reaction-diffusion system under natural conditions on the reaction function and with initial condition $θ$. We show that on the global attractor $\\mathcal A$ of the resulting dynamical system $(u_θ(t):t\u003e0)$, a reverse Poincaré inequality holds true, and that as a consequence the map $θ\\mapsto u_θ(t)$ satisfies a $L^2$-Lipschitz stability estimate on $\\mathcal A$ for any $t\u003e0$ fixed. We then show that statistical recovery of an initial condition $θ$ in the attractor $\\mathcal A$, as well as prediction of the states $u_θ$, is possible from discrete measurements of the system at `fast' near parametric convergence rates.","short_abstract":"We consider a two-dimensional periodic reaction-diffusion system under natural conditions on the reaction function and with initial condition $θ$. We show that on the global attractor $\\mathcal A$ of the resulting dynamical system $(u_θ(t):t\u003e0)$, a reverse Poincaré inequality holds true, and that as a consequence the m...","url_abs":"https://arxiv.org/abs/2606.06018","url_pdf":"https://arxiv.org/pdf/2606.06018v1","authors":"[\"Dimitri Konen\",\"Richard Nickl\"]","published":"2026-06-04T11:06:59Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.AP\",\"math.DS\"]","methods":"[\"Diffusion Model\"]","has_code":false}