{"paper":{"title":"Parameter Estimation for a partially observed Ornstein-Uhlenbeck process with long-memory noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Brahim El Onsy, Frederi G. Viens, Khalifa Es-Sebaiy","submitted_at":"2015-01-20T21:06:43Z","abstract_excerpt":"\\noindent \\textbf{Abstract}: We consider the parameter estimation problem for the Ornstein-Uhlenbeck process $X$ driven by a fractional Ornstein-Uhlenbeck process $V$, i.e. the pair of processes defined by the non-Markovian continuous-time long-memory dynamics $dX_{t}=-\\theta X_{t}dt+dV_{t};\\ t\\geq 0$, with $dV_{t}=-\\rho V_{t}dt+dB_{t}^{H};\\ t\\geq 0$, where $\\theta >0$ and $\\rho >0$ are unknown parameters, and $B^{H}$ is a fractional Brownian motion of Hurst index $H\\in (\\frac{1}{2},1)$. We study the strong consistency as well as the asymptotic normality of the joint least squares estimator $("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04972","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"}