{"paper":{"title":"Parameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ehsan Azmoodeh, Lauri Viitasaari","submitted_at":"2013-04-09T06:34:22Z","abstract_excerpt":"Fractional Ornstein-Uhlenbeck process of the second kind $(\\text{fOU}_{2})$ is solution of the Langevin equation $\\mathrm{d}X_t = -\\theta X_t\\,\\mathrm{d}t+\\mathrm{d}Y_t^{(1)}, \\ \\theta >0$ with Gaussian driving noise $ Y_t^{(1)} := \\int^t_0 e^{-s} \\,\\mathrm{d}B_{a_s}$, where $ a_t= H e^{\\frac{t}{H}}$ and $B$ is a fractional Brownian motion with Hurst parameter $H \\in (0,1)$. In this article, we consider the case $H>\\frac{1}{2}$. Then using the ergodicity of $\\text{fOU}_{2}$ process, we construct consistent estimators of drift parameter $\\theta$ based on discrete observations in two possible ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2466","kind":"arxiv","version":5},"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"}