{"paper":{"title":"Asymptotic stability for a class of Markov semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.PR","authors_text":"Bebe Prunaru","submitted_at":"2011-12-24T12:24:02Z","abstract_excerpt":"Let $U\\subset K$ be an open and dense subset of a compact metric space and let $\\{\\Phi_t\\}_{t\\ge0}$ be a Markov semigroup on the space of bounded Borel measurable functions on $U$ with the strong Feller property. Suppose that for each $x\\in\\bdu$ there exists a barrier $h\\in C(K)$ at $x$ such that $\\Phi_t(h)\\ge h$ for all $t\\ge0$. Suppose also that every real-valued $g\\in C(K)$ with $\\Phi_t(g)\\ge g$ for all $t\\ge0$ and which attains its global maximum at a point inside $U$ is constant. Then for each $f\\in C(K)$ there exists the uniform limit $F=\\lim_{t\\to\\infty}\\Phi_t(f)$. Moreover $F$ is conti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5718","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":""},"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"}