{"paper":{"title":"The Sharp Constant for the Burkholder-Davis-Gundy Inequality and Non-Smooth Pasting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.PR","authors_text":"Florian Stebegg, Walter Schachermayer","submitted_at":"2015-07-28T09:45:10Z","abstract_excerpt":"We revisit the celebrated family of BDG-inequalities introduced by Burkholder, Gundy \\cite{BuGu70} and Davis \\cite{Da70} for continuous martingales. For the inequalities $\\mathbb{E}[\\tau^{\\frac{p}{2}}] \\leq C_p \\mathbb{E}[(B^*(\\tau))^p]$ with $0 < p < 2$ we propose a connection of the optimal constant $C_p$ with an ordinary integro-differential equation which gives rise to a numerical method of finding this constant. Based on numerical evidence we are able to calculate, for $p=1$, the explicit value of the optimal constant $C_1$, namely $C_1 = 1,27267\\dots$. In the course of our analysis, we f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07699","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"}