{"paper":{"title":"Stochastic differential equations with path-independent solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Imme van den Berg","submitted_at":"2012-09-04T12:09:34Z","abstract_excerpt":"We present a condition for a stochastic differential equation dX_{t}={\\mu}(t,X_{t})dt+{\\sigma}(t,X_{t})dB_{t} to have a unique functional solution of the form Z(t,B_{t}). The condition expresses a relation between {\\mu} and {\\sigma}. A generalization concerns solutions of the form Z(t,Y_{t}), where Y_{t} is an Ito-process satisfying a stochastic differential equation with coefficients only depending on time, to be determined from {\\mu} and {\\sigma}. The solutions in question are obtained by solving a system of two partial differential equations, which may be reduced to two ordinary differentia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0623","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"}