{"paper":{"title":"Estimating a periodicity parameter in the drift of a time inhomogeneous diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Reinhard Hoepfner, Yury Kutoyants","submitted_at":"2010-10-25T12:56:15Z","abstract_excerpt":"We consider a diffusion $(\\xi_t)_{t\\ge 0}$ whose drift contains some deterministic periodic signal. Its shape being fixed and known, up to scaling in time, the periodicity of the signal is the unknown parameter $\\vartheta$ of interest. We consider sequences of local models at $\\vartheta$, corresponding to continuous observation of the process $\\xi$ on the time interval $[0,n]$ as $n\\to\\infty$, with suitable choice of local scale at $\\vartheta$. Our tools --under an ergodicity condition-- are path segments of $\\xi$ corresponding to the period $\\vartheta$, and limit theorems for certain function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5105","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"}