{"paper":{"title":"Ergodicity of stochastic real Ginzburg-Landau equation driven by $\\alpha$-stable noises","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lihu Xu","submitted_at":"2012-05-27T19:52:57Z","abstract_excerpt":"We study the ergodicity of stochastic real Ginzburg-Landau equation driven by additive $\\alpha$-stable noises, showing that as $\\alpha \\in (3/2,2)$, this stochastic system admits a unique invariant measure. After establishing the existence of invariant measures by the same method as in [9], we prove that the system is strong Feller and accessible to zero. These two properties imply the ergodicity by a simple but useful criterion in [16]. To establish the strong Feller property, we need to truncate the nonlinearity and apply a gradient estimate established in [26] (or see [24]} for a general ve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5995","kind":"arxiv","version":2},"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"}