{"paper":{"title":"Uniqueness in Law for a Class of Degenerate Diffusions with Continuous Covariance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gerard Brunick","submitted_at":"2011-05-09T23:18:07Z","abstract_excerpt":"We study the martingale problem associated with the operator $L u = \\partial_s u + 1/2 \\sum_{i,j=1}^{d_0} a^{ij} \\partial_{ij} u + \\sum_{i,j=1}^d B^{ij} x^j \\partial_i u$, where $d_0 \\leq d$. We show that the martingale problem is well-posed when the function $a$ is continuous and strictly positive-definite on $\\bb R^{d_0}$ and the matrix $B$ takes a particular lower-diagonal, block form. We then localize this result to show that the martingale problem remains well-posed when $B$ is replaced by a sufficiently smooth vector field whose Jacobian matrix satisfies a nondegeneracy condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1821","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"}