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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1304.2466","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-09T06:34:22Z","cross_cats_sorted":[],"title_canon_sha256":"1ca2b978a410cfdc8c33f102fee7d1753ce8ed9983042fe35b6ae21a9b59537e","abstract_canon_sha256":"8e12a5f7fce21d950514213524f247848b7531cea90ebc17898be5e819b26a0c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:02.664364Z","signature_b64":"dTfg8LiLfcQ08z/dN9h3gnyAl9ZrVR9vV7pFxJ4ovBzC5MptyD7cS6oy7YLuARfjLPM2f3F0H7w8Qa7mtf0PBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcab8ec3e6c24987c4a9a4ff0daac7bfa194c280f75cd90389b255961af31e3b","last_reissued_at":"2026-05-18T02:43:02.663767Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:02.663767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $H>\\frac{1}{2}$. 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