{"paper":{"title":"Coupling of Brownian motions in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Elisabetta Candellero, Wilfrid S. Kendall","submitted_at":"2017-05-23T14:18:38Z","abstract_excerpt":"Consider a separable Banach space $ \\mathcal{W}$ supporting a non-trivial Gaussian measure $\\mu$. The following is an immediate consequence of the theory of Gaussian measure on Banach spaces: there exist (almost surely) successful couplings of two $\\mathcal{W}$-valued Brownian motions $ \\mathbf{B}$ and $\\widetilde{\\mathbf{B}}$ begun at starting points $\\mathbf{B}(0)$ and $\\widetilde{\\mathbf{B}}(0)$ if and only if the difference $\\mathbf{B}(0)-\\widetilde{\\mathbf{B}}(0)$ of their initial positions belongs to the Cameron-Martin space $\\mathcal{H}_{\\mu} $ of $\\mathcal{W}$ corresponding to $\\mu$. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08300","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"}