{"paper":{"title":"Quasi-stationary distributions for randomly perturbed dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Mathieu Faure, Sebastian J. Schreiber","submitted_at":"2011-01-18T10:43:21Z","abstract_excerpt":"We analyze quasi-stationary distributions $\\{\\mu^{\\varepsilon}\\}_{\\varepsilon>0}$ of a family of Markov chains $\\{X^{\\varepsilon}\\}_{\\varepsilon>0}$ that are random perturbations of a bounded, continuous map $F:M\\to M$, where $M$ is a closed subset of $\\mathbb{R}^k$. Consistent with many models in biology, these Markov chains have a closed absorbing set $M_0\\subset M$ such that $F(M_0)=M_0$ and $F(M\\setminus M_0)=M\\setminus M_0$. Under some large deviations assumptions on the random perturbations, we show that, if there exists a positive attractor for $F$ (i.e., an attractor for $F$ in $M\\setm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3420","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}