{"paper":{"title":"On explicit solutions to Ito diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bruno Remillard, Michael A. Kouritzin","submitted_at":"2016-08-18T18:25:24Z","abstract_excerpt":"Strong solutions of p-dimensional stochastic differential equations that can be represented locally in explicit simulation form are considered. The following three-way equivalence is established: 1) There exists such a representation from all starting points, 2) the representation pair satisfies a set differential equations, and 3) the stochastic differential equation coefficients satisfy commutation relations. Next, construction theorems, based on a diffeomorphism between the original equation solutions and the strong solutions to a simpler Ito integral equation, with a possible deterministic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05362","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"}