{"paper":{"title":"Asymptotics of the maximum of Brownian motion under Erlangian sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A.J.E.M. Janssen, J.S.H. van Leeuwaarden","submitted_at":"2013-03-15T13:37:15Z","abstract_excerpt":"Consider the all-time maximum of a Brownian motion with negative drift. Assume that this process is sampled at certain points in time, where the time between two consecutive points is rendered by an Erlang distribution with mean $1/\\omega$. The family of Erlang distributions covers the range between deterministic and exponential distributions. We show that the average convergence rate as $\\omega\\to\\infty$ for all such Erlangian sampled Brownian motions is $O(\\omega^{-1/2})$, and that the constant involved in $O$ ranges from $-\\zeta(1/2)/\\sqrt{2\\pi}$ for deterministic sampling to $1/\\sqrt{2}$ f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3773","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"}