{"paper":{"title":"Energy of taut strings accompanying Wiener process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eric Setterqvist, Mikhail Lifshits","submitted_at":"2014-05-07T15:55:28Z","abstract_excerpt":"Let $W$ be a Wiener process. The function $h(\\cdot)$ minmizing energy $\\int_0^T h'(t)^2\\, dt$ among all functions satisfying $W(t)-r \\le h(t) \\le W(t)+ r$ on an interval $[0,T]$ is called taut string. This is a classical object well known in Variational Calculus, Mathematical Statistics, etc. We show that the energy of this taut string on large intervals is equivalent to $C^2 T\\, /\\, r^2$ where $C$ is some finite positive constant. While the precise value of $C$ remains unknown, we give various theoretical bounds for it as well as rather precise results of computer simulation.\n  While the taut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1651","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"}