{"paper":{"title":"Diffusions under a local strong H\\\"ormander condition. Part II: tube estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lucia Caramellino, Paolo Pigato, Vlad Bally","submitted_at":"2016-07-15T15:05:02Z","abstract_excerpt":"We study lower and upper bounds for the probability that a diffusion process in $\\mathbb{R}^n$ remains in a tube around a skeleton path up to a fixed time. We assume that the diffusion coefficients $\\sigma_1,\\ldots,\\sigma_d$ may degenerate but they satisfy a strong H\\\"ormander condition involving the first order Lie brackets around the skeleton of interest. The tube is written in terms of a norm which accounts for the non-isotropic structure of the problem: in a small time $\\delta$, the diffusion process propagates with speed $\\sqrt{\\delta}$ in the direction of the diffusion vector fields $\\si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04544","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"}