{"paper":{"title":"Optimal Brownian stopping when the source and target are radially symmetric distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nassif Ghoussoub, Tongseok Lim, Young-Heon Kim","submitted_at":"2019-06-25T22:56:55Z","abstract_excerpt":"Given two probability measures $\\mu, \\nu$ on $\\mathbb{R}^d$, in subharmonic order, we describe optimal stopping times $\\tau$ that maximize/minimize the cost functional $\\mathbb{E} |B_0 - B_\\tau|^{\\alpha}$, $\\alpha > 0$, where $(B_t)_t$ is Brownian motion with initial law $\\mu$ and with final distribution --once stopped at $\\tau$-- equal to $\\nu$. Under the assumption of radial symmetry on $\\mu$ and $\\nu$, we show that in dimension $d \\geq 3$ and $\\alpha \\neq 2$, there exists a unique optimal solution given by a non-randomized stopping time characterized as the hitting time to a suitably symmet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11635","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"}