{"paper":{"title":"Least squares estimator for the parameter of the fractional Ornstein-Uhlenbeck sheet","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ciprian Tudor (LPP), Jorge Clarke De La Cerda","submitted_at":"2011-09-05T15:18:13Z","abstract_excerpt":"We will study the least square estimator $\\hat{\\theta}_{T,S}$ for the drift parameter $\\theta$ of the fractional Ornstein-Uhlenbeck sheet which is defined as the solution of the Langevin equation \nX_{t,s}= -\\theta \\int^{t}_{0} \\int^{s}_{0} X_{v,u}dvdu + B^{\\alpha, \\beta}_{t,s}, \\qquad (t,s) \\in [0,T]\\times [0,S]\ndriven by the fractional Brownian sheet $B^{\\alpha ,\\beta}$ with Hurst parameters $\\alpha, \\beta$ in $(1/2, 5/8)$. Using the properties of multiple Wiener-It\\^o integrals we prove that the estimator is strongly consistent for the parameter $\\theta$. In contrast to the one-dimensional c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0933","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"}