{"paper":{"title":"Coupling all the L\\'{e}vy stochastic areas of multidimensional Brownian motion","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Wilfrid S. Kendall","submitted_at":"2005-12-14T17:20:58Z","abstract_excerpt":"It is shown how to construct a successful co-adapted coupling of two copies of an $n$-dimensional Brownian motion $(B_1,...,B_n)$ while simultaneously coupling all corresponding copies of L\\'{e}vy stochastic areas $\\int B_i dB_j-\\int B_j dB_i$. It is conjectured that successful co-adapted couplings still exist when the L\\'{e}vy stochastic areas are replaced by a finite set of multiply iterated path- and time-integrals, subject to algebraic compatibility of the initial conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512336","kind":"arxiv","version":2},"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"}