{"paper":{"title":"Tubes estimates for diffusion processes under a local H\\\"ormander condition of order one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lucia Caramellino, Vlad Bally","submitted_at":"2012-02-21T21:17:03Z","abstract_excerpt":"We consider a diffusion process $X_{t}$ and a skeleton curve $x_{t}(\\phi)$ and we give a lower bound for $P(\\sup_{t\\leq T}d(X_{t},x_{t}(\\phi))\\leq R)$. This result is obtained under the hypothesis that the strong H\\\"{o}rmander condition of order one (which involves the diffusion vector fields and the first Lie brackets) holds in every point $x_{t}(\\phi),0\\leq t\\leq T.$ Here $d$ is a distance which reflects the non isotropic behavior of the diffusion process which moves with speed $\\sqrt{t}$ in the directions of the diffusion vector fields but with speed $t$ in the directions of the first order"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4771","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"}