{"paper":{"title":"Weak noise and non-hyperbolic unstable fixed points: Sharp estimates on transit and exit times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.PR","authors_text":"Giambattista Giacomin, Mathieu Merle","submitted_at":"2013-07-16T12:15:12Z","abstract_excerpt":"We consider certain one dimensional ordinary stochastic differential equations driven by additive Brownian motion of variance $\\varepsilon ^2$. When $\\varepsilon =0$ such equations have an unstable non-hyperbolic fixed point and the drift near such a point has a power law behavior. For $\\varepsilon >0$ small, the fixed point property disappears, but it is replaced by a random escape or transit time which diverges as $\\varepsilon \\searrow0$. We show that this random time, under suitable (easily guessed) rescaling, converges to a limit random variable that essentially depends only on the power e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4255","kind":"arxiv","version":3},"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"}