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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1105.1821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-09T23:18:07Z","cross_cats_sorted":[],"title_canon_sha256":"60a3ebce2d15f0e63c2ecda398795cf3f5251a91d0dc2771902cc7ae62e3e163","abstract_canon_sha256":"a9a44fca40b7f8261bd13e3d0de2e365eae5cad59f41147130a0749ac199976d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:30.479913Z","signature_b64":"hLfot+YQVixfrRfQJarPe5Dwdu+YaxedZKyL6lSE11cURzp/usuPca76rtmRFiDSz1tSYaV/09KSTHDW5E9HDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f62c8c1029e7709e76468ef7e3b9db5edfbd89877cb5d21c7cb3b6ac87b7dc7","last_reissued_at":"2026-05-18T04:22:30.479475Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:30.479475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $d_0 \\leq d$. 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