{"paper":{"title":"On Limiting Behavior of Stationary Measures for Stochastic Evolution Systems with Small Noise Intensity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Jianliang Zhai, Jifa Jiang, Lifeng Chen, Zhao Dong","submitted_at":"2016-11-22T09:58:42Z","abstract_excerpt":"The limiting behavior of stochastic evolution processes with small noise intensity $\\epsilon$ is investigated in distribution-based approach. Let $\\mu^{\\epsilon}$ be stationary measure for stochastic process $X^{\\epsilon}$ with small $\\epsilon$ and $X^{0}$ be a semiflow on a Polish space. Assume that $\\{\\mu^{\\epsilon}: 0<\\epsilon\\leq\\epsilon_0\\}$ is tight. Then all their limits in weak sense are $X^0-$invariant and their supports are contained in Birkhoff center of $X^0$. Applications are made to various stochastic evolution systems, including stochastic ordinary differential equations, stocha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07223","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"}