{"paper":{"title":"Markov bridges: SDE representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Albina Danilova, Umut \\c{C}etin","submitted_at":"2014-02-04T18:28:49Z","abstract_excerpt":"Let $X$ be a Markov process taking values in $\\mathbf{E}$ with continuous paths and transition function $(P_{s,t})$. Given a measure $\\mu$ on $(\\mathbf{E}, \\mathscr{E})$, a Markov bridge starting at $(s,\\varepsilon_x)$ and ending at $(T^*,\\mu)$ for $T^* <\\infty$ has the law of the original process starting at $x$ at time $s$ and conditioned to have law $\\mu$ at time $T^*$. We will consider two types of conditioning: a) {\\em weak conditioning} when $\\mu$ is absolutely continuous with respect to $P_{s,t}(x,\\cdot)$ and b) {\\em strong conditioning} when $\\mu=\\varepsilon_z$ for some $z \\in \\mathbf{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0822","kind":"arxiv","version":4},"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"}