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Mathematics > Probability
Title: Asymptotic expansion of the drift estimator for the fractional Ornstein-Uhlenbeck process
(Submitted on 1 Mar 2024 (v1), last revised 3 Apr 2024 (this version, v2))
Abstract: We present an asymptotic expansion formula of an estimator for the drift coefficient of the fractional Ornstein-Uhlenbeck process. As the machinery, we apply the general expansion scheme for Wiener functionals recently developed by the authors [26]. The central limit theorem in the principal part of the expansion has the classical scaling T^{1/2}. However, the asymptotic expansion formula is a complex in that the order of the correction term becomes the classical T^{-1/2} for H in (1/2,5/8), but T^{4H-3} for H in [5/8, 3/4).
Submission history
From: Nakahiro Yoshida [view email][v1] Fri, 1 Mar 2024 20:33:30 GMT (55kb)
[v2] Wed, 3 Apr 2024 18:34:38 GMT (84kb,D)
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