{"paper":{"title":"Sampling of probability measures in the convex order by Wasserstein projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.CP"],"primary_cat":"math.PR","authors_text":"Aur\\'elien Alfonsi, Benjamin Jourdain, Jacopo Corbetta","submitted_at":"2017-09-15T16:00:08Z","abstract_excerpt":"In this paper, for $\\mu$ and $\\nu$ two probability measures on $\\mathbb{R}^d$ with finite moments of order $\\rho\\ge 1$, we define the respective projections for the $W_\\rho$-Wasserstein distance of $\\mu$ and $\\nu$ on the sets of probability measures dominated by $\\nu$ and of probability measures larger than $\\mu$ in the convex order. The $W_2$-projection of $\\mu$ can be easily computed when $\\mu$ and $\\nu$ have finite support by solving a quadratic optimization problem with linear constraints. In dimension $d=1$, Gozlan et al.~(2018) have shown that the projections do not depend on $\\rho$. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05287","kind":"arxiv","version":3},"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"}