{"paper":{"title":"Tracking a Random Walk First-Passage Time Through Noisy Observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.TH"],"primary_cat":"math.ST","authors_text":"Aslan Tchamkerten, Marat Burnashev","submitted_at":"2010-05-04T19:59:38Z","abstract_excerpt":"Given a Gaussian random walk (or a Wiener process), possibly with drift, observed through noise, we consider the problem of estimating its first-passage time $\\tau_\\ell$ of a given level $\\ell$ with a stopping time $\\eta$ defined over the noisy observation process.\n  Main results are upper and lower bounds on the minimum mean absolute deviation $\\inf_\\eta \\ex|\\eta-\\tau_\\ell|$ which become tight as $\\ell\\to\\infty$. Interestingly, in this regime the estimation error does not get smaller if we allow $ \\eta$ to be an arbitrary function of the entire observation process, not necessarily a stopping "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0616","kind":"arxiv","version":3},"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"}