{"paper":{"title":"On Optimal Stochastic Ballistic Transports","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alistair Barton, Nassif Ghoussoub","submitted_at":"2017-11-30T19:43:40Z","abstract_excerpt":"For a given Lagrangian $L:[0,T]\\times M\\times M^\\ast\\rightarrow \\mathbb{R}_+$ and probability measures $\\mu\\in\\mathcal{P}(M^\\ast)$, $\\nu\\in \\mathcal{P}(M)$, we introduce the stochastic ballistic transportation problems \\begin{align}\\tag{$\\star$}\n  \\underline{B}(\\mu,\\nu):=\\inf\\left\\{\\mathbb{E}\\left[\\langle V,X_0\\rangle +\\int_0^T L(t,X,\\beta(t,X))\\,dt\\right]\\middle\\rvert V\\sim\\mu,X_T\\sim \\nu\\right\\}\\\\\\tag{$\\star\\star$}\n  \\overline{B}(\\nu,\\mu):=\\sup\\left\\{\\mathbb{E}\\left[\\langle V,X_T\\rangle -\\int_0^T L(t,X,\\beta(t,X))\\,dt\\right]\\middle\\rvert V\\sim\\mu,X_0\\sim \\nu\\right\\} \\end{align} where $X$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00047","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"}