{"paper":{"title":"On statistical inference for non-linear dynamical systems evolving in their global attractor","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AP","math.DS","stat.TH"],"primary_cat":"math.ST","authors_text":"Dimitri Konen, Richard Nickl","submitted_at":"2026-06-04T11:06:59Z","abstract_excerpt":"We consider a two-dimensional periodic reaction-diffusion system under natural conditions on the reaction function and with initial condition $\\theta$. We show that on the global attractor $\\mathcal A$ of the resulting dynamical system $(u_\\theta(t):t>0)$, a reverse Poincar\\'e inequality holds true, and that as a consequence the map $\\theta \\mapsto u_\\theta(t)$ satisfies a $L^2$-Lipschitz stability estimate on $\\mathcal A$ for any $t>0$ fixed. We then show that statistical recovery of an initial condition $\\theta$ in the attractor $\\mathcal A$, as well as prediction of the states $u_\\theta$, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06018","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06018/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}