{"paper":{"title":"Robustness of nonuniform mean-square exponential dichotomies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hailong Zhu","submitted_at":"2019-02-12T00:59:10Z","abstract_excerpt":"For linear stochastic differential equations (SDEs) with bounded coefficients, we establish the robustness of nonuniform mean-square exponential dichotomy (NMS-ED) on $[t_{0},+\\oo)$, $(-\\oo,t_{0}]$ and the whole $\\R$ separately, in the sense that such an NMS-ED persists under a sufficiently small linear perturbation. The result for the nonuniform mean-square exponential contraction (NMS-EC) is also discussed.\n  Moreover, in the process of proving the existence of NMS-ED, we use the observation that the projections of the \"exponential growing solutions\" and the \"exponential decaying solutions\" "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04199","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"}