{"paper":{"title":"Integrability of solutions of the Skorokhod Embedding Problem for Diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Hobson","submitted_at":"2014-03-10T11:40:09Z","abstract_excerpt":"Suppose $X$ is a time-homogeneous diffusion on an interval $I^X \\subseteq \\mathbb R$ and let $\\mu$ be a probability measure on $I^X$. Then $\\tau$ is a solution of the Skorokhod embedding problem (SEP) for $\\mu$ in $X$ if $\\tau$ is a stopping time and $X_\\tau \\sim \\mu$.\n  There are well-known conditions which determine whether there exists a solution of the SEP for $\\mu$ in $X$. We give necessary and sufficient conditions for there to exist an integrable solution. Further, if there exists a solution of the SEP then there exists a minimal solution. We show that every minimal solution of the SEP "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2214","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"}